passport renewal in uk and marrage visa

ok. i am currently living in the uk on a limited leave to remain visa. i am getting married this summer in canada but then coming back to england. i will be getting a marrage visa, so that i can have more choice of job.
i need to get my passport renewed aswell so i figured i should just get the new passport in my new name. will this be a problem when i apply for the marrage visa? how can i go about doing this in the uk? (as i have to travel back on my current passport because that is the name the ticket is in).
how long will it take?
will haveing a new passport in a new name affect my current visa?
any sugestions or help would be great, thanks.