I always use a comparison site, then get on to our insurer, Hastings, who invariably match the cheapest comparable quote. I do find it a bit galling though, as they could have offered this price to start with - maybe next time I'll actually switch to the cheaper company.
British Gas Homecare gave me my best win this year. They sent their usual inflated quote (up 70% this time). I spent about two minutes texting them. Was offered a price just 30% more than last year if I accepted a £50 excess. Said no thank you, we wanted to stick with the zero excess. So the next text said, okay, you can keep the zero excess at the same price as last year. Will this be acceptable? You bet it will!
DH suggested I should have said no, I'd like a 10% discount on last year's price. I'll let him do the negotiating next year. 