If arriving with BA from UK you'll arrive into T4S (non-Schengen flights) which will actually mean taking a metro type train from T4S to T4 to collect baggage and exit. On exiting luggage reclaim, exit terminal and you can catch a bus (the only option) that will take you to T1. This is quite a distance, but at least I think the bus goes direct from T4 to T1 before T2 and T3, but journey should be in the range of around 10 minutes if I remember correctly. Waiting for luggage at T4 can take AGES in my experience. Lovely terminal though.
Check-in for Easyjet at T1 can be quick and can be EXTREMELY slow if there are a number of flights, so perhaps getting Speeding Boarding Plus to make use of the special check-in counter may be a good idea if on a tight connection.
I hate to say I think it's going to be quite tough to make your return connection. Arrival into T1 is usually much quicker than T4 (less traffic, planes parked closer to baggage reclaim). EZY usually use jetbridges at T1, but not always.To be honest, if BA does close 55 minutes before, I really can't see you making the connection.
Here's a link to official information on transit bus from AENA / Madrid airport website:
Transit bus - Airport Madrid-Barajas - Aena.es - Spanish airports and airspace