Dear OP,

Funny you mention this, I just posted about the same thing where me and my Mrs just made it, but our bags didn't :/ !

Basically, I don't think 55 mins is enough! Its a shambles. Our flight PMI-MAD T4 was slightly delayed, then we had to wait ages for the jet bridge. The FAs had already told us what gate to head to in T4S. We were in 1A and 1C so straight off and literally legged it (no toilet stop or anything) to the monorail. Got out of the monorail, and got to the passport control station, the queue was LONG! There was a sign which said something like 'Connections Urgent' I went there thinking ok this is good, unmanned. I asked an attendant and stressed we were about to miss our next flight, and he just shrugged and had us join the main line! It was so frustrating...

Anyway we JUST made it by the skin of our teeth. It was so stressful though, we arrived on the aircraft sweating, out of breath, stressed and desperate for a pee! Not what one expects when paying Business Class fares!

Then at LHR, icing on the cake, after waiting half an hour or so at the carousel after cases started coming out, went to the desk to be told ours are still in MAD.

They need to increase the minimum connection time I think, or at least ensure there is a fast track passport lane for people on v tight connections.