OK, maybe “few and far” between is a little bit of a stretch. Looking around, it seems that about 20% of Hungarian vocabulary has Slavic roots, and about 10% German, but about 90% of the words used in Hungarian are native words, which would explain why when listening to or reading Hungarian, it seems like there’s not a whole lot of Slavic loanwords (although some very basic ones, like the words for Wednesday, Thursday, Friday, and Saturday are. Which makes me wonder why those particular words were borrowed, but the other days of the week are descriptive native words. Language is so fascinating.)
There are plenty of cognates, but it would be better not to search for them in a Swadesh list, because cognates at this distance don’t always match up with the same meaning. Words of related meanings carry many of the cognates.
For example, Hungarian egy ‘1’ has been traced back to Proto-Uralic *ede ‘ahead, before’, cognate to Mansi ela ‘forward’, Finnish esi- ‘pre-, fore-’.
The Finnish word for 1, yksi, shares cognates with Erzya veyke, Mansi akwa, Khanty it, from Proto-Uralic *ükte.
As you noted, Hungarian ket ‘2’ is cognate with Finnish kaksi, Northern Sami guokte, Erzya kavto, Samoyedic ketä, all from Proto-Uralic *kakta, which had a front-vowel variant **käktä *(the Hungarian and Samoyedic words being from the latter).
Hungarian *harom *‘3’ is a cognate of Finnish kolme, Erzya kolmo, Mansi khurum, from Proto-Uralic *kolme. The Ugric branch used a variant Proto-Ugric form *kormɜ.
Hungarian *négy *‘4’ is a cognate of Finnish neljä, Erzya nile, and Mansi ńila, from Proto-Uralic *neljä.
Hungarian *öt *‘5’ is cognate to Finnish viisi, Erzya vete, Khanty wet, from Proto-Uralic *witte. The Samoyedic forms of this root (**wüt *in PS) mean ‘10’.
Remarkable how closely Finnish still sticks to Proto-Uralic in the case of *kolme *and neljä.
These authors repeat the “partial creolization” observations of McWhorter,* but then go deeper and claim the changes were so great that Danish/Norse essentially “replaced” Anglo-Saxon as the prinicipal root of English, partly (as septimus mentioned) due to later Danish-speaker influences. I guess that’s a matter of opionion, but it seems a bit of a stretch to me.
*They cite this article, which I summarize see in an earlier post:
McWhorter, John H. 2004. “What Happened to English?” In Focus on Germanic
Typology, edited by Werner Abraham, 19–60. Berlin: Akademie.
Interesting. I would never have guessed with “5” that the Finnishn form is a cognate.
I studied Italian during my gap year. Italian looked to me like a badly spelled version of Spanish. Old Spanish.
Many of the cognates are Spanish words that have either fallen out of favor, or are not part of the day-to-day vocabulary. Any well-read Spanish speaker would understand them.
I studied French for 5 years, and found it much harder than Italian for some reason.
I have traveled to Sweden with my Danish husband. He spoke English even in Malmo, Swedes apparently have a hard time understanding Danes.
Norwegians make fun of Danes: https://youtu.be/s-mOy8VUEBk
The vowels. “OK, so you guys say o and you write eau? Really? And you say Cohn and write Caen? Someone explain this. Or maybe better not.”
As utterly different as *öt *and *viisi *appear—not one letter in common—the derivation of each from Proto-Uralic *witte is not hard to discern. As the etymology explains, the w and i merged into the lip-rounded front vowel ö. Meanwhile in Finnish the phoneme /t/ has a way of turning to /s/ between vowels. Finnish and Hungarian cognates are like two car models that look completely different but run on the same engine under the hood.
I can’t speak for Danish, but Dutch is about halfway between German and English.
I used to have a Dutch family in my school. It drove me crazy when my student would speak to his mother in Dutch. I speak some German and mentally I kept switching gears between the languages and I could almost understand them either way.
Not really. Dutch and German form a language (or dialect) continuum of which English is not a part. English is way too Frenchified for Dutch to be considered a sort of half-way marker between it and German.
I just wanted to highlight this again. As a Swede, this is the truth.
The influence from Scandinavia came less from later immigrants than from residents of the Danelaw who spoke Anglicised Norse. The Norman conquest suddenly changed their relationship with the OE speakers of Wessex from competition to cooperation. The English anti-Norman hero Hereward the Wake was Danish; Queen Emma (who married both rival Kings, Ethelred the Unready Saxon and Canute the Great Dane - *) had a Danish mother. Thomason-Kaufman assert with zero evidence that Scandinavian languages were spoken in the Danelaw for only two generations after initial conquest; could a contrary fact be hidden due to the lack of written records? The rise of London to prominence played a key role in the language switch: it was adjacent to the Danelaw (and had been conquered a few times by the Danes).
(* - And Emma’s brother, Duke Richard II of Normandy, was grandfather of William the Bastard — this relationship to Queen Emma was the basis for the Bastard’s claim to England.)
The transition from Old (Wessex) English to Middle (London) English was a major event with most of the OE lexicon lost. French word borrowings, while high in number, were mostly associated with politics, law, or an upper-class life style; OTOH the ME words from Norse/Danish were of basic words, words where borrowing is less common. When a ME word has cognates in both Old English and Old Norse, it is common for etymologists to assign OE as the source — this is circular reasoning that underestimates the size of the Norse lexicon in English.
But Emonds and Faarlund base their case not on lexicon, but on grammar. They give dozens of specific examples where changes in word error, case assignment etc. switch between OE and ME to resemble Scandinavian grammar, and claim that such changes are rare.
I’ve little formal training in linguistics and may not be competent to have an opinion, but the Emonds-Faarlund book is interesting and seems very well argued.
Right, thank you, septimus – that’s why I wrote “later Danish-speaker influences” rather than “later Danish-immigrant influence.” I understand we’re talking about, say, third-or-fourth-generation English residents of Danish extraction, still speaking Danish in some contexts, or at least still sprinkling their English with heavy Danish vocabulary and, it seems, grammatical constructions.
Of course you would. 
I read in the Danish news that Danish movies are now shown in Danish cinemas with subtitles. In Danish.
Basically, YMMV.
It’s not a perfect analogy, but to get a sense of it, I suppose you could say that the experience of a Norwegian or a Swede listening to Danish is a bit like an American trying to understand someone speaking in a thick Scottish accent. How well this works out will depend on the particular speaker and the particular listener. If you’re American, and you’re dropped in the middle of Glasgow, the lingo that you find yourself surrounded by is unmistakably some form of English, so you figure that you should be able to understand it. But in practice, again, YMMV. Sometimes there’s no problem, beyond the minor issue that this delightful and sexy accent makes you feel all funny in the pants department. Other times, it’s not so easy, and you really have to concentrate to follow along. And then there are those times when you feel like you’ve had a stroke, your brain begins to melt, you start having headaches and hallucinations, and you get an uncontrollable urge to punch someone in the face.
So, a bit like that. I’m actually not sure if the experience is the same the other way around, with a Dane listening to Norwegian or Swedish. Maybe it’s the same sort of thing, or maybe it’s slightly different. I did ask a Dane about it once, but all he had to say on the subject, as far as I could make out, was this. So I punched him. That’s when I had to leave Copenhagen. Maybe I’ll get back to you on that later.
My first experience in Scotland was a business trip in which I had to interact with a lot of Scottish folk, and my experience was whenever someone walked up to me and started speaking, 100% of the time I had to ask them to repeat what they were saying. Once we were talking, and there was some context, my comprehension went up significantly. I still had to ask them to repeat things, but not nearly as much as when starting “cold”. There were definitely vocabulary differences, but it was mainly accent, and even the differences in vocabulary were sometimes comprehensible in context, once the accent was penetrated.
As a side note, I also had to interact with this American guy from Louisiana during the same trip. He was a real Cajun, and I actually found him harder to understand than the Scottish! My experience with Cajun English prior to this was limited to CCR’s Jambalaya. 
French is something of an outlier among the romance languages, I think because of Frankish influences. For instance, look at the words for “thank you”:
Latin: Gratias
Spanish: Gracias
Italian: Grazie
French: Merci
The first three are all very obvious cognates, but where the heck does the fourth one come from?
Well, it comes from the Latin merces, meaning pay or reward. (As, BTW, do a lot of words, such as the English “mercy” and “merchandise”, and probably the name of the god Mercury. But I digress.) Certainly not Frankish. Maybe it was a slangy sort of thing originally? Like when you go to Australia, and the word for “thank you” is “cheers”.
Too late for edit:
Sorry, bollixed the quote box link in the previous post. That was **Chronos **I was quoting, obviously. I had the multi-quote thing checked by accident from earlier, and… anyway. Apparently, when I don’t post much for a little while, I forget how to dope.
Carry on.
Not unlike the US, where the word(s) for “you’re welcome” are “no problem”.
I thought Australian for “thank-you” was “ta”. Which, apropos of this thread, I always figured came from Danish “tak” (or one of the Scandinavian countries). I’m probably wrong about that, but that was my first thought.