It does seem like you have already made up your mind, and I agree, go for it and do it on Tiger Moths. There are only two downsides:
1) They can't handle as strong winds as more boring types.
2) Booking is not as easy as with most places. You'd want to basically book at least 6 weeks in advance to be sure to get slots.
Because of these two reasons and the fact that it is harder to land them than spamcans the license will take longer to get, but as you said, it doesn't matter so go for it.
To me it seems ludicrous that somebody who loves old planes might contemplate wasting their time on some crappy cessna when they could just as easily do it on a Tiger Moth, and to top it all off you even live in Cambridge! I mean it just doesn't require any thought! Go for it!
It took me about 51 hours (in 2 years) to get my license, although the average is somewhat higher. You may get p**sed off doing circuits for ages but it's worth it in the end. Imagine doing your first solo and your first solo landaway in a Tiger. It's as good as you think!
The instructors there are absolutely top notch (the ones i've flown with anyway, 2 main + about 4 others) and this is because they don't actually get paid, apart from expenses, they're there because they like teaching and flying on Tigers. There are no hour building types there. If you need some ground work explained or whatever, you can just get an instructor to help you with it, there's no hourly charge or anything for groundschool.
You will also get to learn lots about the planes themselves and how to swing propellers and everything.
One thing I would say is to not start yet. If you book say once per week through December, January, February then you'd be lucky to fly 2 or 3 times and this will just p**s you off. I'd say start booking up in April when the weather gets nice again. If you want you can just come along and have a look round.
By the way FNG, I didn't have to do an IMC on a Piper, I just did it on the Tiger so I have no spamcan stains on my log book!