That left hand pipe looks to be actually a pipe still with insulation on it. Photo is hard to see clearly though. And the pipes appear to be too shallow a depth?
Initially, on reading the start of this thread I thought, it is only £350 if it satisfies the customer, but reading on I would say DO NOT pay ANY money and DO NOT put anything in writing, text or email without careful consideration and advice.
As already advised, be careful anything verbal isn't being recorded.
I see the story as this, -
(1) You earlier serviced the combi boiler, but yet no phone calls were made to you about pressure dropping after you fitted the toilet. That's a bit odd.
(2) The pipes are below where pan was going, so if an original pan had previously been there, then those heating pipes were always in wrong location and you would be oblivious to that.
(3) The pipes are probably far too close to the top of floor, - would ideally need to be at least 75mm of screed above the pipe insulation.
(4)You used the proper pan fixings, as supplied by customer, and fitted them in correct location in relation to new pan.
(5) You have been informed months later of this allegation and been refused the opportunity to look at and make good anything, should it prove to be your fault.
Note that if you pay ANY money towards the fix, then you can be accused of admitting responsibility, simply by the fact you look guilty paying back money.
Remember judges will only work on evidence or admission of guilt, so keep any wording to just showing concern that the customer should blame you for another plumbers bad workmanship and also fail to contact you.
I think the law does allow for a customer to immediately get another tradesperson in to redo work, if the work has been done to a very substandard - like if a builder built a wall without a foundation, for example. But in that toilet install, it can't be judged as anything other than an understandable error due to previous work from an unknown plumber and even a professional expert (plumber) going to court for the customer would have trouble convincing a judge otherwise.