Yup, Denham is a 20 minute train from Marylebone then a 20 minute walk (21 minutes actually, I always found!). Used to do that every Saturday for about a year.
Biggin hill is not really doable - involves a long and infrequent bus trip.
Personally don't know about Elstree.
I know of an instructor at Stapleford who lives in Kings X and commutes by public transport.
All those arifields have decent places to do a PPL. Stapleford in particular may be good if you are going the whole hog as they have a competitively priced commercial course and mostly very good instruction.
If you drive have you considered buying a really cheap car? - it would make your life a lot easier. You could probably be insured and taxed etc for £700ish including car.