I know Wycombe Air Centre and Wycombe Air Park quite well, you've chosen a good airfield and a good flying school.
If you've substantially done the flying, so it's a case of coming up to the required standards and getting to know the airfield and aeroplane - I don't think you'll struggle in a month.
British weather is very variable, and at that time of year it can be consistently excellent, consistenly unflyable, or somewhere in between. But it's highly unlikely if you are based there for a month that you will fail to get your PPL, and with any luck a bit more flying in besides (have a go if you get really lucky with time at adding a UK IMC rating whilst it's still available, or at-least a night qualification). Also possible on site if you've got everything done quickly - there are tailwheel training, microlight differences training, or gliding instruction all available on the field.
My guess is that on average, over that sort of time period, you have a good chance of flying twice in a day, every other day. So the odds are very much in your favour.
Two warnings about Booker (the local name for Wycombe Air Park); one is that the airfield cafe recently went out of business so you'll need to take sandwiches!, the second is that the local public transport is not brilliant - on the other hand High Wycombe (the nearest town) does have a bus service out the airfield, and the town itself, whilst scruffy, does have a fair bit to do when the weather's crap, as well as being only an hour by train from the centre of London and a reasonably inexpensive place to stay.
Do turn up having already studied for all of your ground exams and ready to take them as soon as you turn up. Also you could do worse than get hold of the local charts and study those before you arrive. The airport diagram you can get online from the UK AIP.
G