I stay at the LHR Renaissance pretty well every week for a couple of nights, so I'm a bit of an expert on this topic (sad but true)

In my experience, if your reservation quotes your MRW number, i.e. you can see the reservation on your account online, then the points will post, usually after 48 hours.

If the number isn't quoted on the reservation, and even if you hand over your card at check in and the number is quoted on your invoice, it simply won't post and you'll have to fax in your invoice afterwards.

I don't know why it works like that, but it does.

M