I claimed a missed departure via a very crappy Lloyds TSB policy underwritten by GE back in the summer and had no problems at all- acknowledged within a couple days, cheque within 4-6 weeks. They did try to screw me for the excess though- it wasn't listed as applying to that section of the policy but following a quick call I had the extra £40 within a week. Even though a LTSB policy it was GE that I dealt with on the phone and I found them to be reasonable... but then again I do have an excessive attention to detail and I sent them just about everything they could possibly ask for with the initial claim form (signed letter from BA ticket desk & public transport that failed, photocopies of timetables etc etc...) maybe that helped.

Just goes to show that not all experiences are the same!