My children are 33 and 30, plus I have nephew of 36, so not that young I suppose. Nephew caught the virus early last year, was quite ill for a time, gradually improved, eventually back to normal.
All three have been fully vaccinated, can't remember when but it was months ago. They felt it was the right thing to do, my girls saw their normally active cousin from the recommended distance when he was recovering but still weak and it upset them. They'd have had it anyway but that prompted them to make arrangements as soon as they could.
I'm the one who has been hanging back but not deliberately, each time I had an appointment something happened to stop me going. However I had the first jab on Monday. When I went to the vaccination centre (part of a high street pharmacy, round the back, near where I live), a couple of people came along and asked if they could just walk in and were told, yes, queue up or come back later. I wish I had known they did walk ins there, spent ages arranging an appointment on the NHS website! Still it's done now.
If any young people mentioned by posters above are really anxious to get the vaccine as soon as possible, it might not be a bad idea to call in on a vaccination centre on the off chance.