The connection is very doable, it's just that you have almost no margin for delays and LHR has not been very dependable during the last few months. If a (paid by the airline) overnight stay in Madrid would not be a big problem, you can go for it.

If there is a delay that causes you to miss your flight, IB would take care of it as the operating carrier.

You get off the plane at T4S and just follow the signs to gates H, J, K. This will involve going through passport control, then down to the train to T4 (use the lifts, not the escalators), connection security checkpoint (where there should not be any line) and on to your gate.

This month there still was a COVID vaccine check when you got off the transit at T4. If you have an EU digital certificate (or a compatible one, like the British pass), they just scan it. If you don't, you still have to fill in a form at https://spth.gob.es/ before your flight and a nurse checks your vaccination cards on arrival, but even this takes no time (I've had to go through this route several times this summer, having been vaccinated in the US, but there are no queues, so it meant less than a minute of extra time).