This is an interesting question. When I was younger, I had no problem eating alone at restaurants. As I've gotten less young, I feel odd doing so. I was even told point blank at one place that if you are alone, we can't seat you.
Therefore, if I must eat alone, I try going at slightly off-hours, like lunch at 12:00 or maybe 2:30, dinner at either 6:30 or 10:00. That said, I will also look for restaurants with bars, because they typically will let you eat at the bar.
I guess ultimately, most restaurants will not be enthusiastic about serving a single diner, for a number of reasons, so I guess my advice would be to post a question here in FT Dining when you plan to go anywhere new, and see what people have to say.