TinTin.
When The Wind Blows. The Plague Dogs. The Animals of Farthing Wood. Watership Down. Danger Mouse. SuperTed. Bananaman.
If we’re doing claymation, Pingu. And, of course, The Magic Roundabout.
If we’re counting claymation, and if we’re counting the UK as part of Europe, I think The Tree Officer counts. (The youtube version is kind of low-res, but the wit and attitude of the film shines through.)
Jan Svankmajer’s work is freakily awesome. Here are some examples of his short films:
Dimensions of Dialogue
There’s this series of animations of Hungarian folk tales that have some cool animation. Here’s one of those videos: The Pussycat Princess.
Last time I checked, the UK wasn’t its own continent yet, so yes we do. 
…The Snowman, Father Christmas, the Waterbabies, Shaun the Sheep, Willo the Wisp… There’s loads and loads of British animation.
Good calls.
I’d particularly recommend The Plague Dogs, though not if you’ve recently lost a pet and don’t want to cry. Watership Down is a true classic, though I guess not everyone’s seen it yet (and of course there was a remake recently).
When the Wind Blows is one of the best films made about nuclear war. Very gentle, but again not to be watched unless you want a bit of a downer.
Recently, I’d recommend the various Julia Donaldson adaptations, such as The Highway Rat and The Gruffalo. They’re based on books that every parent of a child in the UK aged up to about 25 will know, and many grandparents and the kids too, of course, and they’re gorgeous. They’re made by Magic Light Pictures in London and some of them have been nominated for Oscars. I don’t know how successful the books were in the US, but they are very good, and the adaptations seem to appeal to little kids and their families.
Another good London studio makes Sarah and Duck. Don’t judge it by the first picture you see, because the characters themselves are animated in a very simple way, but the backgrounds are luscious, like a work of art, and the stories are bizarre.
There’s also The Mysterious Cities of Gold, which was a Franco-Japanese production and looks like anime. It was HUGE among 80s kids in England. Might not count since it doesn’t see particularly European, but it was great, so I’m going to include it anyway.
Poland is a hotbed for animation, but a lot of it is really weird (or they work for major studios and don’t get credited as a European production). I’d have to ask my daughter for recommendations.
On a different tack, one very old German/British animator I love is Lotte Reiniger, who was one of the pioneers of silhouette animation. Here’s an example from 1955.
British animations tend to be more likely to have already been seen in the US, though, so although I took the chance to big up some shows and films I like, I’m not sure if they’re what the OP was going for. I mean, it’s not like he’s unlikely to have heard of Wallace and Gromit, for example.
(I’m not actually a big animation fan, but my daughter, who’s 21 and an animation student, is, so I’ve watched a lot).
I just remembered a sweet one: Ernest & Celestine.
I’ve known people in the UK to use the term “Europe” to refer to that set of countries on the western part of the Eurasian continent, mainland only, so not including the UK. I could imagine a British doper saying, “Hey! This thread is about European animation. Why are people bringing up stuff from my country?”
Masha and the Bear, a Russian cartoon that’s very popular.
I just remembered an older animated series that my Italian roomie really loved:
La Linea by Osvaldo Cavandoli.
Very well-known in Italy of course, but around the 1980s and 1990s it was also used by TV networks in other countries around the world as a sort of filler in between their regular shows and movies because the episodes are quite short.
Some international classics from my childhood:
Barbapapa (French)
Mr. Rossi Looks For Happiness (Italian, the music was great)
Calimero (Italian)
Loved MCoG when I was a kid, but it is definitely anime. The French half of the production mostly provided a) money and b) the basic plot/story (it was loosely based on a French book). All the key production staff were Japanese and the show was produced and aired in Japan before it was dubbed/edited for French TV.
However, MCoG was such a hit in France, that about ten years ago, an all-French production team made a SEQUEL. I’ve seen clips on YouTube, but I don’t think it’s ever been released in English.
Masha is the Russian equivalent of Goldilocks. 
Back in the '90s I had some videos of ***The Flumps ***(UK) that my daughter loved to watch. My nephew in Moscow (age 2) now loves Bob the Builder (also UK). I suspect he’ll learn to speak English with a British accent.
My daughter is a genuine bilingual. She grew up with English animated series that were not translated into Romanian. When she was about 3 years old, for example, she watched The Secret Show, a British production. It did not run in Romania, but I bought all the DVDs I could find.
My bilingual daughter learned English from me and a Canadian nanny, so she’s always spoken it with a North American accent. But she was always very sensitive to other ones (I used to teach at a language school where a lot of the teachers were from the UK and Ireland). At home, we always listened to the BBC World Service and she would ask me things like “Why does she say ‘cah’ instead of ‘car’?” and “What does ‘meah’ mean?” (As in “Arnold Schwartzenegger went from being a meah [mere] body builder to Governor of California.”)
My nephew’s parents are Russian, but they both speak excellent English with just a trace of an accent. I wish learning Russian had been as easy for me as learning English is going to be for him.
Until she came to live with me at 2 1/2 (at the request of her mother, who was caring for her diabetic father), my daughter spoke Russian almost exclusively. She understood English because I had always spoken it to her, but she could hardly speak it at all.
At the end of two months, she spoke English perfectly. It was like talking to another adult.
Note that not all of them are “made in London”- some aremade in South Africa.
I’ve seen the 2012 MCOG in English (we have the DVD, but I don’t know if there’s an American DVD version). Wikipedia claims it was made in England, which surprises me. The 2016 season was made in France but has been released in English too. The Mysterious Cities of Gold (2012 TV series) - Wikipedia
Magic Light Pictures also claim they made The Highway Rat and the others on that page (so does Wikipedia) and say that they’re a British company. Confusing. Maybe they were a co-production. https://www.magiclightpictures.com/
They’re the main production company, so they paid for it and made production decisions, probably some editing. But the actual animation work for the ones done by Triggerfish was done locally. I know this because some of those animators are my friends or acquaintances. The Environment Supervisor for Highway Rat/CG Supervisor for Zog was in my AfrikaBurn camp, for instance.
The Wikipediaarticle on Triggerfishlists all their TV specials as “for Magic Light Pictures”. You decide whether that means they’re British or South African or both. I consider them “made in South Africa”, myself, as that’s where the animation was done.
My daughter knows some of the Magic Light people, and I’m fairly sure they did do some of the animation. I’d consider it to belong to both countries, really.