Looks like Boots has a Varicella vaccine - https://www.boots.com/online/pharmacy-services/chickenpox-vaccination-service?srsltid=AfmBOop8DfJBAlwnNDK8aFCjS1Ba5gfNWxuZ4sJfY88aaSPFVSWbZeDR - if they wanted to get it privately.
I agree with you though that OP should try and get these vaccinations before the medical with their GP Surgery to save money or get them on the day of the medical for a fee. I asked my GP Surgery about which ones they did offer (just in case) and mine said they didn't really offer any of the ones that I might need. I decided to just let the medical staff on the day of my medical tell me which vaccinations I needed. I ended up getting a Tetanus Booster and Hepatitis B vaccine and I personally was happy to pay the fee.
The Covid booster I got at Boots - Visa Medicals were really good as they offered to hold onto my medical file so I had time to get my Covid booster as there were 6 weeks between my medical and interview. Once I had got that I sent over the relevant proof of vaccination and they updated my medical file and marked it as complete before sending it to the embassy.
Might as well get the vaccines all sorted out before you travel to the USA rather than hold off and still have it on your to do list after travelling over.