The Daughter takes some meds that are not sold here either OTC or prescription in the exact formulation she had in the USA. She is limping along on what is available here. There are some other meds that we use that are OTC in the States but not in the UK. We brought a year's supply of both when we came over, no problem. (Copy of the prescription in hand, just in case it was needed. Nobody asked.) Do keep anything you bring with you in your carry-on, so it doesn't get lost.
You pretty much cannot get anything that might have an antibiotic in it (like neosporin cream) or stronger than tylenol OTC here. It was kind of a shock to find that Naproxin is by prescription here. (Ace bandages are also non-existant, so if you use them you'll want to bring some.)
Since then we've ordered the OTC stuff and had it delivered to friends who were flying over, so we have another half-year's supply. We hope to be back to the States in February (if things work out) and will arrange to get another year's supply and bring it back with us (it has a decently long shelf-life). We will be making appointments with our dentist and doctor in the USA to take care of what needs doing (including getting prescription meds) and will be hopefully good for another year.
We fly in through either Glasgow or Edinburgh when landing in the UK, to avoid LHR and Gatwick. We have had nothing but "Welcome to Scotland" out of anyone when arriving. But, again, to be prepared, have a copy of the prescription for anything that might be a controlled substance. (I know you said they were not - but do check to make sure that they are not in the UK.)