Yes, it varies by out-station. Many easyJet locations don't have a baggage issue, their profile of passengers means it all fits. Other locations, MAN I know about, on certain routes they proactively manage it, like Ryanair, before boarding. Other places they react after the boarding is close to completion, in the way described above. FR are consistent, U2 are not.

But with both airlines the baggage issue is more efficiently handled than BA for a totally different reason: the cabin crew are far, far more pro-active during the baggage storage stage: moving bags around so wheels in first, sorting out inefficient scattering of paper shopping bags, helping old dears, and so on; BA cabin crew are quite passive in comparison.

But overall it's not a palatable approach from a BA passenger point in view: whatever your status/ticket, if you are late to board and there is no space your bag goes in the hold. They want you at the gate well before BA, and they don't do connections. To get priority boarding you may need to stand in a queue for a good 20 or 30 minutes before boarding, whereas BA don't do it that way (though BA passengers often volunteer to do it anyway). Invariably they make you queue before the aircraft has arrived, so if there are landing delays that 30 minutes can easily turn into an hour. I know some people on this forum prefer this approach to "speedy boarding" (sic) but you can count me out!