I'm a contractor also, front end, and my agency invoices for me. All I do is fill out a timesheet on work time. It's literally no different than a perm role, but I get 100k instead of the 50k - 60k I'd get for the same role as a perm.
Recruiters generally aren't interested in you at any advertised rate, or even for any particular skill. They just see Java (substitute as necessary) and contracter in the general vicinity of each other and decide to call you up and smooch you, even if the job is not a good fit and pays half what you charge. Problem is, you often have to keep in touch with recruiters to keep the flow of work, so you can't just cut them off entirely.
Burner phones and email addresses for recruiters is certainly a thing, though.
When I was doing contract from 2004-2007, a shit Nokia and an O2 PAYG phone was a good investment. Many times did I just chuck the thing in the bin.
Recruiters will suck up to you even if you've ignored them for months. Commission vampires - that's all they are. You're just a line in a spreadsheet to them.
My current rate is nearly double the rate of my first contract which was equivalent to double my last permanent salary. This is after a few years of contracting, starting off in a low-cost city (Belfast, N. Ireland) branching out to Dublin and now London.
Also there is a risk of being fired with a one week notice and not being able to find next gig for a couple of month. So 400 is not a lot, it is just an adequate minimum for London.
>and not being able to find next gig for a couple of month
In London? Sure, you could be laid off anytime, but if you can't land a new contract in two weeks then there's something wrong with you. Contract market in London is buzzing.