The question was:
'How do UK flying schools get people through these three week PPLs with our weather, (especially around this time of year?) I'm curious to know!'
The unsurprising answer is not often. In the unlikely event of favourable weather for three weeks (AND if it happens to co-incide with your course dates!), you may encounter other typical UK problems such as limited opening times, examiner on holiday, lack of aircraft availability, instructor busy etc.
So, with everything and everybody in your favour, 3 weeks is just possible in the UK but I agree that the probability is very low
Whatever the location or subject, there are obviously advantages and disadvantages in any quick course and, in any case, not everyone is allowed 3 weeks off work, or their relationship! But it shouldn't be a problem to take your PPL course in more than 3 weeks, as you would probably only have to pay for the extra accommodation.
Some digress, and more now go, to the US, where the probability of completing a PPL course in 3 weeks at one of the British owned JAA schools must be very high. Although it is true that the weather is not always suitable for students, even in Florida or California, the key factor is that it is rarely adverse all day, or for days on end. Also, the bigger established schools are obviously 'geared-up' for 3 week JAA PPL courses, with plenty of aircraft, instructors and opening time. Another advantage at such schools is that students stay there so, if you become behind schedule, you're on standby to fly immediately the opportunity presents itself.
Because flying is very much cheaper in the US and most agree it is a pleasanter place for private pilots, not only do more train in the US but many people now do most, or all, of their flying there.