Not convinced with this. It would be fair to assume that a 10/15 minute break would probably be sufficient to get to a car in a work car park and turn the phone off.
And maybe didn’t think about phone until looking through bag/jacket/pockets?
Maybe. But, I'd say there is significant reason that made it in the murderer's interests to turn the phone off at that time and not hours earlier, i.e. a risk materialised at that time that wasn't in place in the preceding hours.
Let's say Claudia's phone was in a locked car in a work car park, well, it's not a risk because nobody is going to walk past, hear an unanswered mobile and think: I'm gonna have to break into this car because that's probably a murdered woman's phone going unanswered and there could well be a body in the car also. It's not really a risk and a murderer would have known that.
You could come up with 100 reasons within half an hour as to why that phone needed to be turned off at that time but it wasn't a problem to leave it turned on before then, some ideas for a start:
1) The phone was turned off at the time when Claudia's body was being buried (along with possessions). In the event you have a phone in your pocket and you don't answer it, nobody walking past is going to care and you have control over who sees that phone. Upon burying the phone with a body and leaving the area, you have no control over who would stumble upon a ringing phone and start digging. Local man, knew the area well, on an hour dinner break, secluded location about 20 minutes away. You'd probably say that burying a body in broad daylight is a risk, but then so is leaving a body in your car until you can dispose of it, particularly if you have a wife/family and the car keys are lying around in the house. Who knows, maybe the murderer thought it was expedient to get rid of a body as soon as possible.
2) The murderer was leaving York and was well aware that mobiles can be tracked within reason.
3) Claudia's phone was very close to somebody who wasn't involved in the murder but had reason to ring Claudia and could do at any time, e.g. the murderer put Claudia's possessions in his work bag. Then again, you'd assume that he could get to that bag and turn off the phone before a dinner break.
4) Claudia was murdered at dinnertime. She voluntarily or involuntarily went with someone, somewhere instead of work.
5) The phone was found by somebody not connected to the murder. He or she picked it up and later thought this is useless to me, I'll turn it off and hoy it away. Seems unlikely to me, why not just hoy it away.
6) The murderer was going to a place where somebody would care about a mobile phone ringing on his person, e.g. a wife who knew he didn't have a phone and would want to know why a phone was ringing in his pocket.
As said, you/I/anyone else could come up with all sorts of ideas here, but I'd say it really is significant in terms of why 12.10 was a good idea to turn the phone off (and not earlier).