In my experience, every insurance company says they're the cheapest, but, by definition, all but one of them are lying.
Last time i dealt with Adrian Flux they came out with the same talk, i got a quote, and then a better quote elsewhere.
They all say they will beat any competitor - to be honest, im not much interested in that - id rather they just gave me an honest quote to begin with.
In short, i think they are all as crooked as the crooks they claim are increasing the premiums every year.