Yep, my parents have both had their second dose postponed. I work with older people and I only know a handful who have had the two doses within the timescale recommended by the developers.
Having said that, I do agree that the government made the correct call (for the first time in this whole pandemic) to get as many first doses into as many arms as possible and not because it meant I got mine.
When I booked my first dose, after contact from my GP, there was no option to book the second. The same for my partner. I was told at the centre that administered my first dose that my GP would be in touch about the second dose.
I think the latest 'band' of beneficiaries are experiencing a different booking system to earlier bands who were largely called into their appointment by GPs. The 50+ group seem to have a more open self-booking system made available to them. Although I suspect there's considerable local variation.
No matter what, it's been a very impressive effort (and no coincidence that no cronyism has been involved in the granting of contracts for the process)