There are a lot of 'match.com' and other dating websites advertised on trains. I guess that their predominance there is for a reason so you just might be onto something.
London is the key market to get right to make it work in the UK. Once you have London then things should be easy.
Maybe you need to take your idea to some place such as the Metro or Evening Standard. They have a similar vested interest in the London commuter thing and they are losing out to gadgets at the moment. A dating app could serve their interests if it also took people to their online news content. Plus they have the million or so readers needed for the app to get traction. A profile need not be as extensive as on a normal dating site as it would be more about time and place. Once the profile is made then, when you browse the rest of the Metro/Evening Standard (waiting for those dates to come in) then they get a good idea of who might want to sell you ads. Great, more targeted advertising - rejoice!!!
One problem is the 'I am going to be stalked as soon as I get off this train' factor. So you could change the rules so that only men have a public profile and any women can browse the available men, drop a 'virtual handkerchief' and allow the app to reveal their profile to those they choose.
I know it is not 'Neighbourhood Watch'/Suzy Lamplugh fear any more in the UK, however, your dating app could allow someone to have their best friend know where they are when they are on a date. If they were going on a random-train-date then this might be useful.
If you watched that Panorama programme on dating websites - and the fake profiles - you will know the dating website business model. This is to have subscribers paying for as long as possible, i.e. not finding dates. If you follow HN you will know about the advertiser funded 'Plenty of Fish' and how much money was to be made there by not having the 'classic' model.
Returning to The Metro, they already have a feature where people can have messages about 'the guy with the whatever on the 185' and so forth. If a similar per-train message board existed, of which extracts were in the Metro, then that could be an idea...