Personally I would not recommend travelling via tube or train after surgery. I was advised by the LVC also not to do this. In the end I stayed overnight in London, I was tempted not to but I am glad I did. Whilst the procedure itself was completely painless and a lot less of a big deal than I had built it up in my head, there was no way I was up to being able to travel.
Your mileage may vary. I came out of surgery and layed down in their 'quiet room' and initially there was no discomfort. After a while they took me back to reception and I sat with my girlfriend waiting for a taxi back to the hotel. The lights felt bright, and I felt physically drained (probably just from worrying). The taxi seemed to take forever, by the time it got to the LVC my eyes were streaming with tears but still no pain. You're asked to wear sun glasses, I'm glad I did - it felt so bright outside and I must have looked like I'd had the worst news ever what with all the tears.
The worst part of the entire process for me was the few hours immediately after surgery, laying in the hotel room. The only way I can describe it is feeling like I had acute hay fever behind my eyes. I couldn't lay still, and there was just a really weird 'sensation' - I can't describe it. All I wanted to do was have a really good rub of my eyes which of course you can't do. My nose got blocked up and I was fidgeting around for hours. You have to put drops in every 15 minutes, they give you a timer which goes off what feels like every 2 minutes lol it was a real struggle to even open my eyes, and the tears plus the drops made things really difficult!
As I said this might have been just me, you might not get any of this but in summary I am so glad I stayed overnight I would not have felt up to travelling or doing anything else other than laying on the bed lol. Having said all this, I should say that not once was any of this 'painful' it was more just uncomfortable, like ants in your pants but for your eyes. After a few hours it seemed to wear off, nose cleared and eyes stopped streaming, and all been well since