Lots of people go into restaurants by themselves. Food critics, undercover agents, businessmen, tourists, And single men.
You could always ask for a seat in a corner somewhere out of the way. Just add a cloak and a pipe, and you could be one of those Rangers! People thought Strider was strange, but he's the only one who bagged an elf chick. At least in his time.
And if you decide ahead of time who you're going to be, there could be a number of reasons why you show up alone. Maybe your date stood you up. Maybe you've been under a lot of stress at work and need some alone time. Or if you really, really feel the need, you could be the creepy guy sitting by himself who makes everyone uncomfortable just by his mere presence.
Come to think of it, you look a bit similar to one of my cousins. Last summer he went hiking and camping all alone along part of the Appalachian Trail. All alone except for many black bears and the occasional American! Sure, you might bump into an American in a London restaurant. But a black bear? I think not.
If you really want to go to London, then go for it. And after you return you can share some pics with us.
But if you see any black bears, run home!