You can ask, but in my experience and opinion, it is unlikely that your offer will be directly transferred to the London office.
For decades, firms with regional offices have had to deal with people trying to game the recruitment process by applying to offices they think will be less popular, in the hope you they can then do what you are suggesting. This may not be your intention and you may have just changed your mind as to which location you want to work in, but the problem you have is that too many people try to do this at various stages of the recruitment process each year and by default you are associated with those people.
Apart from a straight yes/no decision, the firm could do/say any of the following:
- You'd have to reapply for the London office to be considered in that talent pipeline and benchmarked against them.
- You'd have to start the interview process again with London based lawyers (to me this is the most likely outcome)
A straight yes is more likely if you are an exceptional candidate and someone they don't want to lose, but even then if it is something you want, then re-interviewing with London lawyers should be something you are happy to do. A straight no is if they have already filled or ringfenced their London opportunities or if they just have a strong policy not to allow such requests (I know enough firms who have such a policy).
You'll need to have a conversation with the grad rec team. If they do consider it, they will probably want to know why this wasn't raised earlier in the recruitment process (why you didn't ask to be transferred ahead of your interviews) and what has caused you to change your mind to the location you now want to work in.