We give you exactly what you're looking for below - but before you rush off to browse those results, can we gently suggest that instead of looking for the closest literary agent to you, you ought to be looking for the agent who is going to deliver maximum value for you and your manuscript?
That might mean someone who lives close by . . . but it's just as likely to be someone, based a long way away, but with a particular passion for the themes of your novel or non-fiction. That passion and belief is the single thing most likely to drive the eventual sale of your manuscript.
Remember too that, although most literary agents do work in, or very close to, London, they're there for a reason. All the large UK publishers are based there, so agents are simply trying to stay close to the people they sell to. All British agents will happily handle work from writers anywhere in the UK or Ireland - indeed, nearly all of them will handle clients from much further afield too.
Finally, it's worth bearing in mind, that you won't spend much time with your agent, except, most likely, when things are particularly busy between you and your publisher. And since your publisher will almost certainly be based in London, you will most often see both your agent and your publisher on the exact same visit.In short, we're not sure geographical selection is a great filter to apply, but since you asked the question, here are the answers . . .