When I was in T5 this past week, there were no Barclays ATMs...at least that I saw - and I wandered around quite a bit while waiting on family to arrive. There used to be one in T2, but T2 is currently a construction zone and I do not think there are any ATMs right now.
The closest one I know of is across the street from the Hatton Cross Tube station (first eastbound stop leaving LHR). I am a BoA customer and completely understand the interest in using Barclays.
Where are you headed in London? I can probably advise on the one closest to you. You can always use a credit card to get train fare (if you're traveling by train/Tube) and then use a cash machine near your hotel. Barclays machines are all over London.
robin