Don't book two hour lessons. I've never yet met a student who could concentrate for more than an hour and a half in the early days of training, and some can't manage an hour. I teach on helicopters, which is perhaps slightly more intensive, but I have a PPL(A) too, so I know it's not all that different. If your instructor is any good, he'll be pushing you pretty much to your limit all the time, and you can't keep that up. I've abandoned lessons before now as the student obviously couldn't cope with any more - that's not a criticism; everyone is different, but there's no point in my wasting someone's money and time.
However, two one-hour lessons on the same day is a good idea. Or even three, but I tried that in my early days of training and found it too much...I simply couldn't take it in. If your instructor's good with people, he'll start to know when you're reaching your limit, but a lot of instructors are young and inexperienced...and anyway, you've got to learn this sort of thing yourself someday, so it might as well be now. Flying is all about learning about yourself, more than about manipulating the controls.
As has been said, when you can't fly, do other flying-related stuff. Study for the exams. Learn all you possibly can about navigation and weather - you can never know too much. Go down to the airfield, borrow the POH (pilot's operating handbook) for the aircraft you're flying, and read it thoroughly. You can never know too much about the aircraft you're flying either. Listen to the radio, chat to instructors, listen to more experienced pilots' conversations and join in if you can; overall, simply immerse yourself in the flying world. You'll pick up more than you realise.
In summary, don't make the mistake that many of us make in the beginning in assuming that flying hours are what count. The more study and preparation you do, the better you'll be able to make use of your flying time - so the less it'll cost you overall. You don't fly a certain number of hours and then miraculously get a licence...you get it when you're good enough. That often relates to the preparation and study you've done. And if it doesn't....well, then you're in real trouble, because you won't know enough from just scraping through the exams to cope when you're out there on your own anyway.
Above all, quit panicking. Unpredictable weather is normal in the UK. You're going to be going through this scenario for the rest of your flying life. And you can get lovely weather in the autumn and winter...like we had a wonderful spring this year. Or you might not. You have to get used to it, so you may as well start now.
Or....you could move to Australia or Los Angeles instead.
Good luck,
Whirly (instructor grounded due to weather, so lots of time to post on threads I've never even looked at before)