Read threads on here and ask others.
However, reputations can soon sour and sometimes improve.
Have you noticed that the once great Carole Nash is not so great. Higher prices and poor service is reported. Mrs Nash no longer owns the company. It is part of the very large Ardonagh Group so the call centre person reading off the screen may have been answering a call about someone's pet cat before your call.
https://www.ardonagh.com/about-us/business-portfolio/ardonagh-retail/
Bennetts used to be on a lot of people's avoid list but they seem to have got better under the ownership of Saga. Ardonagh tried to buy them as well but it was fortunate that the Competition Authorities told them to fúck off, so Saga still own Bennetts.
Bemoto has had a lot of good press here but there is noise that they are not quite as good as they used to be. They have a notice on their website apologising for delays in answering calls. Presumably they have expanded beyond a point where their infrastructure can cope.
As for dealing with call centres for a claim. Your contract is with the underwriter so bin the broker and go direct to the underwriter unless you want to be locked into a claims handling process with a shower of cúnts like 4th Dimension paying the broker a finder's fee. This will most likely speed up your claim and mean you can get the repairs done at a place of your choice.
