Prescriptions meds into the UK from the USA in pharmacy bottles?

Yes. Original packaging is preferred by HMRC but is not absolutely essential.

I have never read any report of an ordinary traveller having any difficulty entering a developed country because they were carrying the typical medications dispensed by a pharmacy. On most occasions, one's baggage is not opened and checked at all. Customs officials are on the lookout for narcotics, not heart medicine.

What would you expect them to do? Confiscate something you needed for survival? Send you back on the next flight?

We travel all over Europe and Asia year around and carry meds in their pharmacy packaging in our carry on and have never had a problem anyway. We were in England for the Chelsea Flower Show's member's day recently with meds and visited friends in Wales and relatives in Ireland carrying meds. I also carry along a written prescription for meds that I can fill there if I need to.

There may be some meds which are more strictly regulated in Europe. The problem would vary with what and how much you are talking about. I wouldn't take a giant 500 pills bottle for a two week trip which might result in much time wasted avoiding those sarcasm-laden scenarios mentioned above. I would take a bottle with a two or three week supply and split it when I got there just in case one got lost.

Some meds do have street value (T3s come to mind) so if you are carrying quantities that greatly exceed your needs then, in the unlikely event you are questioned, you may have some 'splaining to do. And if you look like a typical middle aged tourist with middle ager meds and middle ager plans, then it's less likely to cause you to be subjected to vigorous questioning.

You could bring a prescription with the generic name on it. The prescription wouldn't be valid but a pharmacist in Europe could tell you if you need a doctor's prescription and be able to direct you to a doctor or clinic in case you lose/run out/sell your pills none of which are recommended.

I had to get antibiotics twice in Europe. Once was a bad bronchitis after a month of travelling on the cheap and without enough fresh fruit and too little sleep. The other involved in finding a doctor in a little town in Brittany on a Saturday and then dealing with the language barrier. I now travel with antibiotics for that problem as it does occasionally recur and is debilitating when it does.

And carry your meds with you rather than putting them in a checked bag. You don't want them to be stolen or lost.

And if you bring in large quantities of acetaminophen you might be thought a suicide risk ... they are only sold in small packets here.