MotoRinzler,
If cheap is your moto, and you intend to fly predominantly in the UK. then I'd recommend double checking the figures including flights, accommodation, local transportation, additional flight fees, visa fees, food fees etc... You must assume that you will not achieve the PPL within the 45hours stated, aim for the average which I believe is 50 - 60 hours (highly dependent on your ability of course) this may add 1 or 2 weeks to your planned timings abroad. Then add the few hours familiarisation to UK airspace, (and if required as not EASA school UK RT, skills test, class II medical and ground exams) And compare these with local prices. You will most likely find very little difference. When I did the maths, it was actually better to learn in the UK despite the higher costs per hour.
If however, you're looking at weather and time in which you can actually achieve the 45 hours, then perhaps abroad may be a better option - but, you could look at places in Spain or Italy which are EASA countries, and then come back to the UK, do a few hours to familiarise yourself with UK airspace. I think it would be considerably cheaper than crossing the Atlantic... but i may be wrong.
Hope this helps!