I'm not sure how lucky you are going to be in finding someone on here who happens to know all their councils waiting times - particularly ones that are nearby to you.
I wouldn't hold out hope you're going to get a reply that tells you the answer.
I would suggest you pick up a phone book tomorrow first thing and start ringing round. I'd suggest you make the earliest appointment you can with your local council first though so that you don't end a fruitless search to find the next appointment is now 6 weeks away!
Based on my local council - who have a nice brochure showing all this:
http://www.buckscc.gov.uk/assets/conten ... ochure.pdf
They say you have to give 15 days notice, but that to do that requires an appointment, and to get married requires a further booking. So - let's assume you were able to give notice tomorrow - and get married on the 16th day - then you'd be married on the 12th.
I know, from recent experience, that they have (at that particular council) about a week lead time on appointments for things like notice, births etc - so that would push it to the 19th.
You have a further problem to keep in mind - the week of the 25th is a 3 day working week - with easter on one end and the royal wedding on the other. Bucks council do seem to do weddings on a bank holiday - but charge £300 for the privilege and I'd bet they are fully booked already - particularly the Friday!
I'm sorry to be the bearer of bad tidings - but I suggest you get your behind in gear tomorrow am and get the earliest appointments for everything you can.
M.