In UC, you should get a red "fast track" pass for the immigration queue. Having said even, arriving from New York a few weeks ago, even the fast track immigration queue was bad, although no where as bad as the regular main queue.

You need to allow for the morning queus at Heathrow Terminal3. (Mind you have arrived on a Sunday evening at BA's Heathrow Terminal4 with worse queues than I have ever seen at Terminal 3). Not wanting to cast aspersions, but if you have passengers from a flight originating in India or Africa in front of the queue, get out your reading material and be patient!