Resources for expected length of security queues on a given day?

I'm sceptical that you'll find truly useful current data. I saw one site that claimed to have current data, but seemed to be non-functional. Anyway the problem is that the state of the queues now is not sufficient if you live any distance from the aiport - you need to know what they are going to be an hour or two in the future.

Hence what we really need is a reliable model. To help with that you could look at the published performance figures. You will see that for the most part the security delay is 5 or 10 minutes. I have travelled through Heathrow on many occasions in the last few years and never found departure security to be an issue.

However:

1). The check-in process, especially if you have not been able to check-in online and/or have lots of luggage can be slow.

2). An exceptional event (strike, security alert) has the potential to disrupt anything. Hence have a look at the current news and Heathrow website before you leave home.

I normally follow the 3 hour international, 2 hour domestic policy, and have never yet had any problems other than spending too long in the air-side restaurants.

One other thing to bear in mind: the other very unpredictable factor is any delay in actually getting to Heathrow. Both road and rail can suffer disruption, the roads around heathrow can get very slow if there are problems on adjacent motorways, always check the state of the transport system you want to use. I'd consider this to be a far greater risk factor than departure security.