GA insurance is a much smaller market, comprising of only about 5 underwriters, and they don't like pilots that shop around, so if you ask 20 brokers for a quote (like you might do for a car) you will get one or two quotes and an angry response from the rest.
The premium depends a lot on the hull cover; this is similar to a fully comp car cover. But there are differences: with car insce you never get a payout of more than the lesser of the insured value and the market value (and the payout is adjusted downwards anyway if the MV is more than the insured value, so they have you by the g00lies) whereas with aircraft insce you can get an "agreed value" cover where the insce co. will pay out the actual agreed value.
Obviously the cost of insuring a £300k plane, for the full hull value of £300k, will be a lot more than insuring a £20k plane.
As a rough indication, a 50 year old sole pilot with a PPL and with 500hrs might pay £1000-1500/year, plus the cost of the hull cover which runs very roughly around 1% of hull value so a £200k plane will be an additional £2000. In practice he will pay some £4000 initially for the £200k plane.
Unlike the USA, the premium is not much affected by pilot ratings and hours, although there are indications this is changing and a CPL and an IR do help, as might 500-1000hrs.
The NCD system also works differently from cars.
Personally I would just go direct to Haywards. Their premiums are similar to anything else one is going to get, as far as I have been able to see.