The authorative source would be Transport for London's website at
Tube: You can take a folded bike anywhere and anytime
Dockland Light Rail: Can be used on all DLR trains, at any time
London Overground: Are accepted on London Overground trains at all times
TfL Rail: Can be taken on TfL Rail trains at all times
Trams: Trams only takes folded bicycles
Non folding bikes have time restrictions or are fully excluded.
Here's a bike-centric map for NON-folding bikes provided by TfL, dated May 2018. http://content.tfl.gov.uk/bicycles-on-public-transport.pdf
As for your question of what defines a folding bike?, that would be the mechanism of folding. A bike whose main frame has any form of hinge would class as a folding bike.
You'd want to go out of your way to fold it as small as possible. Remember a train is not a public place, and the "terms of conveyance" will permit them to exclude you. So I'd suggest always turning the handlebars and lowering the saddle to make it look smaller. I'd suggest not fitting bulky accessories too, a rack might be convenient but adds to the bulk.
You should absolutely consider a cover or water cape for the bike, to keep its dampness or oils from upsetting anyone. Purchase of some folding pedals, or easily-removable ones like the MKS commuter pedals would be worth considering too.
Another interesting observation - the image above shows the FRONT wheel is removed from the fork and laid beside the rear wheel. I'd bet this bike is not a lot larger than a 20" folder when properly buttoned up.
How you stand/sit with the bike may need some consideration. If you stand and have a backpack, then front-carry the bag on your chest with the bike on the floor below your bag. This would save floor space.
Summary: Rules say you're allowed a folding bike, then you're allowed any wheel-size on a folding bike.