Your first sentence makes no logical sense to me at all, sorry. You can walk in to places all over the country to have a jab or make an appointment online. My brother is working as a volunteer 'jabber' and seems to be busier than ever.
Where are these places that recommend only a 3 week gap? The government wanted to reduce the time to the second jab to 4 weeks, but the scientific advice is not to. I can find this:
In a new study, funded by the Department of Health and Social Care (DHSC), researchers have found that when compared to a four-week gap, a 10-week interval between the doses produces higher antibody levels, as well as a higher proportion of a group of infection-fighting cells in the body known as “helper” T cells.
However, when all the "pros and cons" are taken into consideration - such as soaring cases of the Delta variant and society opening up - eight weeks is the optimum interval.
(ITV News website dated yesterday - others similar on the Telegraph, Guardian, Sky, BBC etc websites)
So waiting the extra four weeks (as opposed to 4) gives better protection - although 10 might be better still. Which is surely what we all want?