If you live in Dorset you have nothing to worry about, you will get a place in either Camden or Mary B. They tend to give the College Grove places to the international students and those who live far away, so you stand a good chance of getting them.
There doesn't seem to be a distance or time limit as such with regards to giving halls places, but the rough rule of thumb is if you live within the M25 you won't get halls. If you live within an hours train of london you're at risk, same if you live on the London side of herts, beds, bucks, essex, etc etc (ie all the counties bordering London/M25).
Of course, nothing isguaranteed and if you have exceptional home circumstances they will take these into account, but if you live very close always have an alternative in mind.
I didn't get halls ( i used to live in outer north west london) and so for first year with only (I think) about 6 weeks notice I had to find somewhere else to live. The RVC do publish a list of names of people who didn't get halls and through that list, and through TSR I found some people to live with (one was kent, one west london, one surrey). I ended up in a really really nice house, where I stayed for second year until the move up to Hawkshead. I know most people didn't struggle to find somewhere to live in second year but be prepared for either not very nice housing close to campus or living slightly further away for nicer house/cheaper rent.
I think I covered everything, feel free to ask if not.