I personally sat on a GNER Mk4 coming back from Edinburgh and had GPS confirm almost 140mph north of Peterborough, in an attempt to make up time (we'd been delayed quite heavily not long after leaving Edinburgh on what was the last King's Cross train of the night).
Given GPS had been happily recording speeds of up to 125mph, I have no reason to doubt its accuracy. Even if it was out by a bit, it wouldn't be out by 15mph and for a consistent distance.
Maybe the driver was illegally speeding, but given it was so long ago I doubt anyone will get in trouble over it. If there were measures in place to stop the train speeding, they can't have worked!
I can't provide proof, so you'll have to take my word for it. Call me a liar if you want, but GPS chipsets have been very accurate for some time, and while some can spike, that's obvious and easy to filter. The only real issue with GPS is the delay, which means you may have a reading that's a little late - but it's still correct.