Oh mate. You ask the unanswerable. How long is a piece of string? All I can tell you is that it took me 14 months to do my PPL in the UK and I had roughly 2 or 3 lessons booked every week - and I'd say more than half of them were cancelled due to weather. Looking at the weather for the last week at my local airport, I'd suggest at least 4 of the 7 days have been unsuitable for PPL training.
I don't know what other chaps will think but I reckon 2 months in the UK is a very ambitious target. It does depend where you are flying from though - for example at Leeds which is built on a hill you will have more cancellations than somewhere on the south coast at MSL.
V2