It does seem to have got worse in the last few years - not that I go to a GP often (maybe once every 3 or 4 years) but I was used to getting an appointment within 1 or 2 days and the last time the only appointement was about a week away.
However, it is worth noting that recent published statistics (for 2011/2012) show that:
"85 per cent could see or speak to a doctor or nurse within two working days compared to 90 per cent in 2009/10."
Note that this is for NHS Scotland - there actually isn't a single NHS for the entire UK.
http://www.scotland.gov.uk/Publications/2012/05/8250/3
One of the problems with the NHS is that it seems to suffer from having regular waves of (probably very expensive) management re-organisation inflicted on it in efforts to make it "more efficient" - often with non-medical managers being incentivized on performance, so they end up gaming the metrics.
Still, I think the NHS and the concept of "free at the point of delivery" championed by Nye Bevan "In Place of Fear" are still fantastically important to society the UK - though nobody claims it is perfect. Clearly the absolute best level of individual care are to be found elsewhere (probably in the US). However, when I see quotes elsewhere in this thread such as:
"I broke my knee this spring but didn't go to a hospital on my families request because the last time I broke a bone I reset it myself and the hospital still charged $8k."
Those pretty much fill me with horror/fear that anyone has to put up with that - which is precisely the reason the NHS was created.