Just to echo some of the comments on here, it's generally better to hang back at the Concorde Room for a bit longer than head to the gate (not least because flights that first flash 'boarding' on screen rarely start boarding at that moment).

If the flight is departing from a B gate then you could always head to the lounge in the B gate area (it's a very nice lounge) a little before boarding time, then you're close to the gate and can wait until it says 'flight closing' to head down.

I wouldn't push to the front of the priority queue. It's simply rude in my opinion. If you're keen to get on board early then maybe re-think the above approach to be at the gate when boarding first starts (when the gate agents will usually invite First and BAEC golds to board first).