My DH is 60 in May and will wait to be contacted like any other considerate person
There are two parallel queues - the mass vaccination centres/national booking service, which you book via the website, and the local GP call up system. You can book via the website first, because they have more slots available. There is nothing wrong with people checking if they are able to access the system, because eligibility will vary by area, depending on how quickly the mass centres are getting through the priority groups.
Your GP will call up any patients in priority groups who have not had the vaccine elsewhere. This obvious takes time, as it’s labour-intensive, and there will be a lot of housebound/frail patients who couldn’t get to a mass vaccination centre.
My DM waited to be called by her GP (because she can walk to the GP, but would have r to take public transport to our local mass vaccination centre, and this was back in late Jan when case numbers were higher). They called her three weeks after she could have booked an appointment via the website.
If people want to wait for their GP to ring them, of course they can. But it uses more resources, and there is nothing “selfish” about using the website instead - it is what you are meant to do. Or it wouldn’t exist.