I don't believe so. They've undoubtedly got various performance measures for the various police forces, but I don't think they have a simple arrest quota for individual officers. If they did have to ramp up their numbers, then I think it'd be an easy job for a cycling officer with a camera to go around and capture all the blatant phone use. Unfortunately, when Avon&Somerset police (my area) provide a positive response to video submissions, they use a standard phrase like "As a result of this report I can confirm a positive outcome in that the driver(s) identified in the submission(s) will receive either a warning letter, a fixed penalty or a prosecution." which doesn't provide much feedback as to what action they are taking (a warning letter is barely an action though I do think they're a good idea). I have also had responses where they also mention a possible NIP (notice of intended prosecution).
As a counter-example of police just looking to make easy arrests, there plenty of reports on https://road.cc where certain forces (e.g. Lancashire) seem to bend over backwards to not take any action on cyclist submitted videos. It's a bit of a lottery as to which areas take things like close passes seriously or not.
But as I said, the average is not necessarily representative at all. Also, at least one of the sources would benefit from showing the problem to be bigger than it is.
> they have little incentive apart from the obvious traffic safety argument.
Do they not have ticket quotas like US cops?