I used to spend the entire day in a large city on my own at 13. Else I lost the will to life staying at my Grandparents. Used to get one bus in and a different one back (to see my fav great aunt). No mobiles and I knew absolutely no one in town.
At 14 we used to get the train from home and shop all day in Swansea. No changes, but no leeway on missing the only train home.
DD1 (15) hasn't had that sort of freedom (although school let them lose in theme parks) because somehow it isn't something she and her friends have wanted to do. Spend all day hiking the ten miles between their houses across country Yes go shopping no.
Try and get him to keep his phone and money in an inside pocket- After watching professional pickpockets in action I trust nobody. I would also make sure he has your phone number written on paper in case he does mislay his phone.
I have no concerns at all about him managing to sort out trains and find his way around. My only fear is that he'll dick around and misbehave. It's a small fear. I think he'll rise to the challenge.
There's some great advice on here. I will talk to the other boy's mum, make them text when on the second train, and I like chocolatespider's idea about explaining that any future trips would depend on how well he was able to handle this one.
He's very competent and desperate for some independence.
It's during parenting moments like this that I remember this poem which describes these small acts of letting go so powerfully.
If your only worry is him messing about, then let him go. The consequences for messing about would hit him quite hard - i.e. getting thrown out of TP and spoiling his day, or getting thrown off a train and having to wait around for an hour - but from what you say, they wouldn't put him in danger. When kids are inclined to be silly, I think it's good for them to learn that silliness has limits - ones that have nothing to do with mean old parents or teachers! - and that they need to be responsible for their own behaviour.
It's a long way for a 13 year old. I would say no without hesitation but offer a less challenging alternative as a compromise. Also don't forget if you say yes to this then next time his request will be more outrageous ambitious.