I used moneymarket.com last year to get insurance for my BMW 330Ci and the lowest quote I had was with Admiral, which did surprise me being one of the bigger companies so I plumbed for them. A year later, renewal came and although it was cheaper I still looked on the net and got two quotes cheaper but didn't quite have what I wanted. So I rang Admiral, spoke to a very polite lady, told her the details from the other quotes, mixing the best bits from both to try and get a better deal from her. A short silence as she had to speak to her "supervisor" and then she came back, way cheaper than their quote, cheaper than anyone on the net and also over a longer term. All for the sake of a phone call. Lesson learned - never accept what is put up in front of you but haggle. In my case it certainly worked and saved me £75 and got me two extra months.
And by the way, as for Direct Line who don't use price comparisson sites I can see why. Absolutely way way more expensive than what I pay now, in fact nearly twice as much. So use the net and the price sites and get the best deal for you.