What actually happens on the day of completion? Would it be possible for my brother to pick up the keys for me or is there something that I'd need to do in person like sign something?
Nothing is signed, that all happens on exchange. Formally your lender would probably be unhappy about someone else picking up the keys but I don't think an estate agent would care.
What actually happens on the day of completion? Would it be possible for my brother to pick up the keys for me or is there something that I'd need to do in person like sign something?