We are a Brit/US couple and live mainly in UK (30 miles above London) so it works the other way for us . We get Easyjet from London Luton (10 miles from home) to Barcelona. Then fly AA from FLL to NYC (where we stay for a while). then back to UK on Virgin using my mileage (19500miles each. Unlike most carriers, Virgin will sell one way)
You will have to come into London from LA, either to Heathrow or Gatwick. Virgin are pretty competitive and, in case you aren't aware, a return will almost certainly be cheaper than one way. Either use your cruise company or Brit Rail (www.thetrainline.co.uk
) to get from Dover.
Perhaps you can find a one-way on Priceline.
Any other UK related questions, get in touch.
Roger & Bryan