This is an interesting and evolving area, but in my experience the verdict usually fall towards the freelancer having legal right to use their own sound effects library as a work-for-hire.
As a freelancer, if you purchase the royalty-free right to a sound effects library and are hired by a company that does not have their own library, you can use your own ...
You can start by getting a network identity. Stuff like a cool name/brand, logo, professional website can only help.
Once that's done you can start researching your market and emailing possible clients. It's a lot of work and for a few months (or years?) won't pay off, but if you keep at it it will eventually start working for you.
I personally have no idea what UK rates are.
Having said that - Sometimes studios have rates that they will generally pay freelancers or a series of rates based on budget, experience and what your tasks are.
Flying there - Are they paying for room and board or are you flying in on your own because you need the project?
Do you know what a standard staff ...