I could see maybe a tiny number of true idiots thinking that, but about the same number as those who think east anglia is a foreign country. It’s not as if northern ireland isn’t ever in the news, and I mean regular news including sports, not just highbrow political stuff.
I can’t tell you the precise number it’s just something many people I know have encountered while in England and farther afield. It’s probably a small minority of English people. I think some people with no direct connection to the island make no distinction in their heads between Ireland and Northern Ireland. It’s not a big deal and the analogy of Qatar/UAE etc. used upthread is a good one. Geographic/political ignorance is widespread. I, for one, couldn’t name all but a few English counties, and I’d have a hard time pointing out on a blank map where many major British cities are.
It used to be the United Kingdom of Great Britain and Ireland. In the 1920s, when the southern part of Ireland became the Irish Free State, and then the Republic of Ireland, it changed to UK of Great Britain and Northern Ireland.
Some counties (I think Argentina is one) have schoolchildren start the day by singing the national anthem. Prayers may be involved in countries with a greater religious influence in public schools (England has alot of state-funded religious schools, Ontario as public Catholic school districts). AFAIK the US is the only non-totalitarian dictatorship where schoolchildren normally obliged (& their teachers) to affirm their loyalty to the state with a pledge or oath every day.
I’ll just pop this in here, seems sort of relevant. Enjoy! 
Dearest creature in creation, Study English pronunciation.
I will teach you in my verse
Sounds like corpse, corps, horse, and worse.
I will keep you, Suzy, busy,
Make your head with heat grow dizzy.
Tear in eye, your dress will tear.
So shall I! Oh hear my prayer.
Just compare heart, beard, and heard,
Dies and diet, lord and word,
Sword and sward, retain and Britain.
(Mind the latter, how it’s written.)
Now I surely will not plague you
With such words as plaque and ague.
But be careful how you speak:
Say break and steak, but bleak and streak;
Cloven, oven, how and low,
Script, receipt, show, poem, and toe.
Hear me say, devoid of trickery,
Daughter, laughter, and Terpsichore,
Typhoid, measles, topsails, aisles,
Exiles, similes, and reviles;
Scholar, vicar, and cigar,
Solar, mica, war and far;
One, anemone, Balmoral,
Kitchen, lichen, laundry, laurel;
Gertrude, German, wind and mind,
Scene, Melpomene, mankind.
Billet does not rhyme with ballet,
Bouquet, wallet, mallet, chalet.
Blood and flood are not like food,
Nor is mould like should and would.
Viscous, viscount, load and broad,
Toward, to forward, to reward.
And your pronunciation’s OK
When you correctly say croquet,
Rounded, wounded, grieve and sieve,
Friend and fiend, alive and live.
Ivy, privy, famous; clamour
And enamour rhyme with hammer.
River, rival, tomb, bomb, comb,
Doll and roll and some and home.
Stranger does not rhyme with anger,
Neither does devour with clangour.
Souls but foul, haunt but aunt,
Font, front, wont, want, grand, and grant,
Shoes, goes, does. Now first say finger,
And then singer, ginger, linger,
Real, zeal, mauve, gauze, gouge and gauge,
Marriage, foliage, mirage, and age.
Query does not rhyme with very,
Nor does fury sound like bury.
Dost, lost, post and doth, cloth, loth.
Job, nob, bosom, transom, oath.
Though the differences seem little,
We say actual but victual.
Refer does not rhyme with deafer.
Fe0ffer does, and zephyr, heifer.
Mint, pint, senate and sedate;
Dull, bull, and George ate late.
Scenic, Arabic, Pacific,
Science, conscience, scientific.
Liberty, library, heave and heaven,
Rachel, ache, moustache, eleven.
We say hallowed, but allowed,
People, leopard, towed, but vowed.
Mark the differences, moreover,
Between mover, cover, clover;
Leeches, breeches, wise, precise,
Chalice, but police and lice;
Camel, constable, unstable,
Principle, disciple, label.
Petal, panel, and canal,
Wait, surprise, plait, promise, pal.
Worm and storm, chaise, chaos, chair,
Senator, spectator, mayor.
Tour, but our and succour, four.
Gas, alas, and Arkansas.
Sea, idea, Korea, area,
Psalm, Maria, but malaria.
Youth, south, southern, cleanse and clean.
Doctrine, turpentine, marine.
Compare alien with Italian,
Dandelion and battalion.
Sally with ally, yea, ye,
Eye, I, ay, aye, whey, and key.
Say aver, but ever, fever,
Neither, leisure, skein, deceiver.
Heron, granary, canary.
Crevice and device and aerie.
Face, but preface, not efface.
Phlegm, phlegmatic, ass, glass, bass.
Large, but target, gin, give, verging,
Ought, out, joust and scour, scourging.
Ear, but earn and wear and tear
Do not rhyme with here but ere.
Seven is right, but so is even,
Hyphen, roughen, nephew Stephen,
Monkey, donkey, Turk and jerk,
Ask, grasp, wasp, and cork and work.
Pronunciation (think of Psyche!)
Is a paling stout and spikey?
Won’t it make you lose your wits,
Writing groats and saying grits?
It’s a dark abyss or tunnel:
Strewn with stones, stowed, solace, gunwale,
Islington and Isle of Wight,
Housewife, verdict and indict.
Finally, which rhymes with enough,
Though, through, plough, or dough, or cough?
Hiccough has the sound of cup.
My advice is to [not] give up!!!
-The Chaos, by G. Nolst Trenite, aka Charivarius (1870-1946)
Are they actually english people though, or people in england? I mean, it’d be understandable if some immigrants or migrants didn’t know.
Though there’d be a pretty high number of english people who’d probably do worse than you at placing cities on a map. 
Prayers are required in all public (comprehensive, for the Brits, public means the exact opposite of what it does in the US because “public”, individually funded schools were designated as different from the parochial ones) schools in England daily.
Except that since six months before Pearl Harbor plunged us into World War II, mandating that students in a tax-funded public school recite the Pledge of Allegiance has been illegal as a violation of their freedom of speech (West Virginia State Board of Education v Burdette).
But that would give the game away. In Connecticut they pronounce "Thames with a “soft” th as in “this”, and with a long *a]. They don’t pronounce it “TEMS”
Yup. That is part of the joke, all right.
“State”, not “comprehensive”. Comprehensive means non-selective, not publicly funded (though comprehensive schools are publicly funded). Public also doesn’t mean the exact opposite of what it does here; public schools are those which are members of the Headmasters’ and Headmistresses’ Conference, not all private schools.
And no, not all the public schools require daily prayers, though all of them are nominally attached to the Church of England.
Thanks for that. It was informative in addition to being rather entertaining.
Actually, western Virginia is south of West Virginia.
There are thickos everywhere, though.
Just look at how many people in Ireland think Brit = English.
Yeah definitely. I posted that comment more to point out it doesn’t seem that big a deal to me if someone from beyond these islands wasn’t aware.
It’d be less remarkable if a new immigrant to Britain wasn’t aware of the complicated geopolitical situation on the islands. I’m talking about actual English people. As I said above, if you don’t have ties, I just don’t think it’s on a lot of people’s radar. For example, my friend was in a bank in Middlesbrough when he emigrated and the bank clerk was flummoxed that Ireland was a different country and had a different currency. My cousin who has lived long term in Manchester has told me about numerous misunderstandings of the same nature. I’m not saying most people in Britain don’t know, just that there are plenty of people who are ignorant of the situation since the '20s. 
Ireland is in most respects not treated as a foreign country so you can forgive the locals for being confused.
There are plenty of foreigners, like the Qataris and Pakistanis in the OP, who think that UK = United Kingdom = Great Britain = England.
Etymologically, though, it’s Wor-cester-shire.
Well she got to Belfast alright. Had the meetings. Got the work done.Due to the success of her meeting, she does now need to go to the Republic. In September.
They’re required to host a “collective act of worship” by law. Though, as wiki points out, they don’t and the EU law supersedes it anyway. You’re correct on the “exact” opposite clarification: they’re a member of a set of the exact opposite (individually funded schools), but don’t encompass the entire set of individually funded schools. Likewise, I forgot the name of the set “state school”, which is what a comprehensive is a member of. There are government administered specialist or charter schools in both countries that have selective requirements as far as I’m aware. It’s compounded by the fact that in the US state schools refer to universities (and the US distinguishes between university and college, where in the UK a college would be for grades 11 and 12).