Yes. There is no restriction, as far as the airlines are concerned, on how much medication you bring in your carry-on bag. In fact as noted above you're advised to not put medications, prescription or OTC, (or any other valuables) in checked luggage due to the risk of loss or theft.

Some countries may have restrictions on what quantities of medication you can bring in, such as no more than needed for your visit or so many days worth, which can vary. In the US, TSA screeners may hassle you - contrary to their own stated rules - on liquid medications in carry-ons (ask for a TSA supervisor if you run into trouble with a screener). It's good practice to be sure and keep prescriptions in their original containers with the Rx label - some countries are sticklers about that.

Also note that some medicines that are available OTC or by Rx in other countries may be illegal or controlled in the US. I had to throw out some very good OTC cough syrup I got somewhere before arriving back in the US, as the main ingredient was considered a controlled substance in the US.

Anyway, back to your specific trip, here is a link to the UK government page about bringing goods into the UK and when you'd need to declare certain items. The UK is fairly easy compared to come countries in terms of medicines (and customs in general) but be sure and check their information to see if anything applies to your specific circumstances.

https://www.gov.uk/government/public...ling-to-the-uk