if the owner did register it they can mark it as sold on the Brompton site - which I guess may allow you to register it in your name. If it is etched and/or listed on BikeRegister (which the Met Police bike markers do) - then there is an option for the owner to 'transfer' the registration over. When you list on Bike Register, you can print off a log book. I guess a tea leaf would have to be pretty determined or very sly to go to the lengths of making up an account (as it is only via email), so it isn't foolproof, but equally many users of expensive bikes are listed on there, so it is one option. You can report a serial number/frame number as stolen with Brompton, so it is worth checking their database.