Hello hiraeth,
Sorry for not having got back sooner. I have been looking into bits and bobs that I have access to. I can't see that William was given a pension as he didn't serve in the Force for long enough. I was at TNA today and had a look in the Police Orders but couldn't find out anything more than to confirm that he left when he did.
I've just had a quick look and remembered the police Service Records which may state more about his service record; including his leaving - which could be under MEPO 4/370. If I remember next time, I'll have a look for you, but if you know someone else who's going they might be able to order it and look for his warrant to see if it includes further information surrounding his leaving, which might help. Or TNA have an online ordering service - if you want to give it a try.
Hope that gives a little help, BarnabyP