I've got absolutely nothing against price comparison websites (or Martin Lewis's site) but anyone who insures their car through a broker, rather than directly with an insurance company, might already be getting the best price anyway.
For example, a few years ago Post Office Insurance (which is a broker, not an insurer) gave me their best quote when my car insurance was due for renewal. I decided to follow Martin Lewis's advice and check all of the various price comparison sites, as well as firms which aren't on them (such as DirectLine). After spending the better part of two whole days on the task, I still couldn't get a lower quote than the one that Post Office Insurance had given me in the first place.
When my car insurance was due for renewal this year, the quote offered to me by Post Office Insurance was a bit lower than what I'd been paying last year, so I simply went along with their offer.