As far as HMRC is concerned you can register yourself as self-employed any time within the first three months of working. The benefits issue is more tricky though and I think you could do with talking to someone who deals with that stuff and can advise you on where you stand, perhaps at the Jobcentre? You can say you want to be a mobile beautician or life coach or something rather than escort.
Working from your home does carry risks, including horny men showing up drunk and uninvited late at night, and getting evicted. A lot of people do it without much trouble though, so read around and ask questions if you're considering it.
There are various alternatives to working at home.
1. Just do outcalls. This reduces your potential client base, but it can still work quite well. If you live in a town where people often come for business or near an airport, there'll be men wanting you to visit them at their hotels. Some people also like you to go to their homes. If you don't like the idea of doing that alone (I don't), try to find a reliable driver who'll wait outside for you.
2. Get a separate working flat. You can rent on your own or with another escort, but this probably isn't something you'd consider yet.
3. Sublet a flat or room. Some people will let you use their place for a daily or hourly fee, which can give you flexibility and also security if they're around while you work.
4. Book hotel rooms. Some hotels will let you cancel on the day of arrival with no penalty, so if you don't get any bookings you don't have to go. On the other hand, if you keep an eye on the travelodge website you might be able to get very cheap rooms in advance