So how do all the bikes get into central London?

While there are certainly some areas like the City of London which are almost exclusively commercial/office, most of London, even the central parts, is a mashup of different land uses including residential. Not everyone commutes in from the suburbs.

Lots of stations have large cycle racks. They just go from office to station and back again.

You can take them on overground trains, though that's kind of restricted at rush hour. I imagine people mostly either cycle from their homes or leave the bike near a station.

Not sure I understand your question. I think people cycle them in…

Folding bikes are sometimes not allowed