It's perfectly possible to own a handgun in the UK. As I said there are significant restrictions but ownership is not barred. You might want to have a look at the legislation proper (the 1997 Act). People are often surprised by what they find (particularly when the discover that the Act does not explicitly refer to handguns).
Well, technically, yes, there are some handguns it is legal to own, but it is a severely restricted category. For example, nothing with a barrel shorter than 30cm.