Whatever it is, it would have to be either desperate or very confident to use HQ in that way, especially since, as an invader, it wouldn't know what it was up against.
Plus, if it was in the Cafeteria, it would probably have been able to hide out for some time sapping energy slowly, but the massive power outage all at once implies that it's due to the drainer of that power suddenly deciding to perform a task requiring lots of energy rather than needing it simply to continue existing.
It probably shouldn't be from the Doctor Who universe; he's fought the Weeping Angels already, and it wouldn't be fun just to see him running down a list of Who nasties. An entity such as an Osmosian would have the motive to sap HQ's power, but they're human-sized, as are most species like them in fiction, and their power-sapping ability just wouldn't be enough to knock the whole grid out, and even if it did, it would only be for a few seconds. If the power drainer is some sort of artifact, there'd be more explanation than it's worth figuring out why it's in the Cafeteria and why it only activated now as opposed to earlier or later than it would probably be worth to introduce it.
With that in mind, I've got a few ideas, but they're a bit shaky. Metroids and Stargate's Replicators are known for their energy-absorbing powers, especially the former, and they are both driven by a need to produce more like themselves. If a Metroid Queen or a powerful enough Replicator got into HQ, it would have been able to enter the Cafeteria(this part would be easy for the Replicator, as most models are quite small) and heal itself on whatever it's drawing the energy from. After it's done, it would increase the process, in preparation for reproduction.
If this goes on, the Metroids could be relocated, but the entire stock of Replicators would have to be destroyed. We can't have Replicators going back to their home canon with any knowledge or power whatsoever from more advanced continua than theirs, let alone HQ. Just them learning what androids were practically wiped out human civilization; learning about plot hole transport could easily break a galaxy..
There are other species that the same idea as above or a similar one could work with, but it's late and I can't remember them all.
I had another two ideas for why the power might be being drained, but one was, I now realize, a blatant ripoff of the Cataclysm part of Legends of Metru Nui, and the other I can't think of any species examples for. The latter one basically amounted to some entities forcibly draining HQ's power to restore their own, or build themselves physcial forms, or something of that sort. It's a bit cliché, and not at all finished, but I don't have a better one right now. I probably will later, though.