Here's all the options that'd be available that I can think of, I'm sure there probably are more, but these are the ones that immediately come to mind:
The Glasgow Subway is the only non-TFL one with fully longitudinal seating, and the interior is a bit dated on them. The system is also fully underground, so will not be suitable if you require mobile phone signal for this
As mentioned above, the South Western Railway (SWR) class 455 units have a section of longitudinal seating and look modern. These trains operate local services from London Waterloo to Guildford, Dorking, Epsom, Hampton Court, Woking, Kingston, Chessington South and a few other places - if you were to go to somewhere like Vauxhall or Wimbledon to wait for one you'd only be waiting a few minutes as there are plenty of them.
The Tyne and Wear Metro trains have multiple sections of longitudinal seating in every carriage, and also look pretty modern. Most of the network is above ground, and in my experience the Metro tunnels have phone signal anyway, so that wouldn't be an issue.
Alternatively, have you considered using a tram for this? The trams in both Edinburgh and Birmingham have sections of longitudinal seating.
There's also the Northern Rail class 150s which have a section of longitudinal seating in one carriage, however I've not been able to find a photo of that.
All photos from this post are from the internet and not mine.
I hope this post helps
