Wait until you're married, then send them letters with your original marriage certificate (or authenticated copies, dont know how to get those though). Dont forget about your national insurance too. Banks you can just walk in with your passport and marriage certificate and get it changed there and then, so you dont have to wait ages for them to send the certificate back. I haven't changed my passport yet, as I've used it to prove my maiden name, but as both names are on the marriage certificate you could prob change your passport whenever you want. If you want a passport in your new name to go on honeymoon with, you can get one in your new name up to 3 months before your wedding date. It will be posted dated though, so only valid from your wedding date.
(i went on honeymoon in my maiden name as the tickets were booked in that name. If you've booked them in your new name you will need to get your passport changed. Also, if they can tell you just got married and your traveling in your maiden name they may not let you travel)