Could a flat tyre two days later be due to a clumsy service? I had my bike serviced on Monday. Part way through the workshop called to inform me that they thought both tyres were perished and needed replacing. I trusted their judgement and gave them the go ahead.

It was fine on Tuesday and Wednesday. Today - Thursday - I got it out this morning and discovered the front tyre was flat. I re-inflated it and rode to work and it seemed fine. But it was completely flat again by lunchtime, so it's a slow puncture.

I haven't ridden any out of the ordinary routes, nor am I aware of having ridden over anything that would cause a puncture. So, obviously, I'm now wondering if the service might have had something to do with this.

I don't want to take it back to the workshop and start throwing accusations around without some evidence. So is this likely just coincidence? Or, if there's a significant chance they might have damaged the tube while replacing the tyres, is there anything I can do to prove it?
To me, this sounds like coincidence. If the shop had punctured the tube and caused a leak, I don't think it would have held air for two days before showing any signs of going flat. Especially given the fact that you reinflated the tube and it went flat again by lunchtime. The leak is fast enough to make the tube go flat in just a few hours, so it seems unlikely that the tube would be OK for Tuesday and Wednesday and only start leaking on Thursday. When replacing the tube, you should look for the cause of the leak. You might be able to find a foreign object that caused it, but it's possible you won't with a typical puncture. If you find the side of the tube leaking, that might indicate that it got pinched by the tire during installation