I was actually advised to do exactly that by an agent at Aplan insurance who said to get a quote for a start date in 28 days and pay for the policy (or the deposit) in advance.
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I had a bad experience with my van insurance last year. Other insurer wouldn't pay out despite police report and dash cam footage being on my side. My insurance were not interested as I didn't have legal cover so had to do everything myself.
3rd party insurance (aviva) dragged it out hoping I'd go away and even got a forensic accountant to analyse my earnings, bank records etc. It took me 18 months but I got my money.
Since then I've switched everything to NFU and Carole Nash. They're really expensive but they pay out and don't charge for extras like amendments.