If the trains are as crowded as you say, any 16" folder is going to be way too big. The floor space it takes up will be one less person who can fit on the train.
Only a Strida or A-Bike would work in that situation.
How far does the train go? Is it realistic to bike the whole way on a full size folder or stiffy? How about purchasing a scooter? I hear those are popular in England... (won't help with slow traffic like the train will though)
Maybe this is a silly question, but can you find out who to write to about boosting the train service? I suspect they don't listen too well, but a letter a week might help. Maybe a petition.
Public transit is one area I thought Europe really has us beat. I thought major European cities were really up-to-date on keeping those systems useful.