Best/quickest way to transfer in Heathrow from T4 to T1

In Brussels yesterday and today. Being clever and knowing that I would be finished at lunchtime and not wanting to wait for the night Aer Lingus flight home (lucky because I see it is delayed to at least 2330 tonight) I decided to bmi it to London and again to Dublin. Arrived at airport to find bmi cancelled (probably due to the weather etc. bumpty bump and all that). Got on a BA to Heathrow which landed in T4 . Went the flight connections route to T1 which involved a bus and an HOUR long queue in security to get to T1. Would a better option on arrival in T4 be to get out into the Arrivals Hall and hop on the Tube to T1,2,3? As it was I was cleared 3 times through security today all with a resultant queue and delay. Okay I got home earlier but I would say I was more frazzled!!

hansov said:

and an HOUR long queue in security to get to T1.

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If you are in a rush for a flight and ask nicely then they will often let you clear security through the priority channel normally not accessible to plebs like us.

I know I saw that there was a 'priority' queue. I was being honest here - I wasn't running late for a flight, had buckets of time but would rather spend those buckets (read pounds sterling) in shops rather that a senseless queue for me as I had to exit into T1 anyways to get my boarding card. (NO Clubman do not say go down to the Irish gates (70 odd to 80 odd) and check in with bmi there - I did and there was nobody person-ing the desk). So I had to track back to T1, out into departures, get a boarding card and queue in Security for my third time today (second time in Heathrow) to go to gate 82.
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Exit from T4 through to landside and then take the Heathrow Express to T123 (it's free for the short hop) - you can take the tube too but you have to pay for that.

It's likely quicker than going through flight connections where as you say the queues can be awful ... the queues to get from checkin through security to the Irish gates in T1 are in my experience never that bad (I can't think I've ever been waiting more than 10 mins)