srw
It's a bit more complicated than that...
My immediate thought was "Brompton". My second thought was "Bakerloo line". Since you already have a Brompton I'd be inclined to use that. I don't know the Hampshire line at all, but on the assumption you can choose a seat because you're starting towards the start of the train's journey, choose one near enough to a lobby that you can use a cheap cable lock to lock it in plain sight to a handrail.