Firstly on getting work rights. I'm assuming that you are a US citizen, which means that you'll need a work permit to work here.
Trying to get an airline to sponsor you to a UK work permit is a complete non-starter: there are always enough similarly-experienced British pilots out there, currently many hundreds of whom are unemployed.
The easiest way to get round this is to hurry up and marry your fiancée (who I am assuming is a UK or EU citizen), which would get you a work permit without the requirement of having to be sponsored by a company.
Now onto licence conversion.
At your experience level you're looking at doing the full ATPL theory course with no exceptions (14 exams, 8-12 months distance learning or 6 months full-time classroom-based), the CPL conversion (length at the schools discretion, expect minimum 5 hours) and the MEIR conversion course (absolute minimum 15 hours). Add in an MCC course which is virtually a pre-requisite for the airlines here.
Budget £2,000 for the theory course, at least £2,000 for the CPL, £4 - 5,000 for the IR, plus at least £2,000 for all the CAA fees. MCC courses range from £2,000 to £5,000.
In total you'll be doing well if you get much change from £15,000
Of course all the above does not include living expenses.
If you want to instruct you'll have to do the full instructor rating course - £5 to 7,000.
Welcome to the expensive world of the JAA!
As for type ratings, well, no, you shouldn't have to pay for one. But people are buying them, and are gettign jobs off the back of them, certain airlines have set a precedent that they require them prior to considering people for jobs. So if you decided to do one, you can add on another £7,000 to £22,000 depending on what type (the range I've given here is SD33/SD36 to A320).
cheers!
foggy.