why don't you tell wanadoo you want to start with them in 30 days and cancel your bt for that same period? The worst sistuation would leave you with no internet for a few days.
This is waht happened when I switched from telewest to pipex, no internet for about a week, but hey!that's all right!
The only problem was telewest, trying to get through the cancelation department, I had to kid on I was leaving the country!
Why don't you check pipex, they're cheap, lost connection once in 1 1/2 year, check their website, look for pipex in this forum.