Thanks to everyone, this is really helpful.
A bit more detail.
The original quote was for piles 2.5 m deep. I was very busy and distracted at the time, and just didn't notice the discrepancy. Also at the time I knew nothing whatsoever about piles, or foundations, or engineers reports. I felt the contractor was trustworthy, and he had been recommended by my architect, so I let him get on with it.
The piles were were put in four months ago. A couple of days before the piling company arrived I was asked to pay £7600 'for the piles', which I did. The piling company left and work continued. I was given an updated estimate/invoice for the job a little later which still showed a figure of £7600 for the piles, together with my payment.
The new figure of £18,300 for piles 6.5m deep was not mentioned until a couple of days ago, after I finally let the contractor go after three months of really shockingly bad work, and asked him to return the money he was holding on account (I don't think I'm being a difficult client, the work really was terrible).
I know from experience that the guy is a liar — effortless, constant and fluent with no conscience whatsoever. My suspicion is that he was concealing the true cost from me at the time the piles were put in, because he suspected (correctly) that if I knew I would cancel the project as my budget was quite tight. So he intentionally provided an incorrect estimate, thinking he would keep the project on track and recoup later. I suspect it's something like that, because a normal, non sociopathic person, if they were about to spend £10,000 of someone's money, would ^%&@ing well ask them first, or at least tell them after.
The piling contractors were on site for one day. Rich pickings. I'm in the wrong line of work if that's worth £18,000...