As announced by the Starwood lurker over on flyertalk, if you register at spgpromos.com/insider you can earn a bonus 2015 spg points on your next stay before the end of the year! It'll need to be a qualifying stay (so not an award booking, not one booked with an OTA etc), but it doesn't matter if it's a pre-existing booking or not. You just need to have registered at spgpromos.com/insider before you checkin. From the look of it, checkin needs to be after 30th November, and checkout on or before 31st December. Only a one-time bonus, but a nice bonus none the less! Could almost be worth a cheap mattress run for, especially if you're very close to requalifying / hitting the next level. BRGs with Starwood (Best Rate Guarantee) get you either 20% off or 2000 spg points, so a cheap stay with a successful BRG claim and this offer could net you a nice slug of points. Probably much easier in the states or asia though, as the UK Starwood properties tend to be a little more expensive, but worth a quick look if you'll be near something suitable.
I know that I was able to make some very cheap Hilton mattress runs over the Christmas/New Year period a couple of years ago. I'll see if the same thing applies here.
One of the Sheratons at Heathrow is often pretty cheap on the SPG Hot Escapes list, but never down to the levels of what some US-based properties seem to manage at very quiet times. The Aloft at Excel seems to be something like 65 quid some nights around Christmas. It'd be a lot of time on tubes and DLR, but you could potentially hop between the two if you were short on stays to requalify...
When I worked in Oxford, I would often stay at either of the Heathrow Sheratons, as both have appeared on the promos list. I would also stay at adjacent properties, e.g. HI Ariel and use the Sheraton for meals (earning in both schemes). For my new job, Aloft is closer. In fact I "stayed" there when a rail strike was "on". As it happens, the strike was called off, so I was left with a non-cancellable stay. So I visited, nicked the consumables, had my free drink and left. The one other benefit was that I qualified for SPG points on all subsequent Uber rides.