when i got mine done ( new car ) i needed to get it taxed too, so gave them all the docs with the old plates still on the car, got a new tax disc and they printed out a revised mot cert then they send out the new v5 in the post. She said you have to put the new plates on straight away, but can't imagine it will matter that much!
i phoned the insurance before i went and told them i'd transfered the plate and asked for them to email me a cover note, took the cover note with old and new plate just in case