How old do you have to be to watch a PG movie alone in a movie theater?

Any age. In both the US and UK, "PG" means Parent Guidance Suggested. Not Parental Guidance Mandatory. Same thing with PG-13 in the US. PG-13 means parents are strongly cautioned about letting a child under 13 see the movie. Again, it does not mean that a parent is required to attend the movie with a child if they're under 13.

So you can go to a PG movie (or a PG-13 movie) alone at whatever age your parents feel comfortable with. There's no age restriction for a PG movie, but most parents don't let their 10-year-old children go to the movies by themselves, anyway.

Just for reference: in the US, rated R means a parent or guardian is required to attend the movie with you if you are under 17. NC-17 (aka Rated X) means no one under 17 admitted, even if they have a parent with them.