It's not a bad idea, certainly an aggressive marketing method.
I don't think I would use it though, I think there is too much risk of coming a cropper. If this is a large 'area' you could end out pricing against one of the larger, national companies who could well be pricing peanuts to get in there themselves, then you are left having to go 15% lower still.
If you are only talking about a price of 20 quid then it wouldn't matter if you make a bit of a loss to get a shoe in the door, but that changes the more expensive the job gets.
It could also smack somewhat of desperation too, you'll do anything to get the job.
If I priced for a contract and found that I was the cheapest of several, I'd be gutted, ditto if I was the most expensive (wouldn't get the job of course) but if my price was in the middle somewhere I'd be happy.
And then my presentation of quote, promise of quality and so on would add to my competitiveness.
If I lost out to the cheapest quote, would I be bothered?
Not really, I don't want customers that simply go for the cheapest quote come what may, because in 12 months time that job will be back out to tender and you will have to price all over again.
good luck to you if you give it a go though, and I agree with Mark, the word - verification - would be much better than proof.
Ian