Are there any types that can NOT fly gear down, land flap, 160kts at 4 miles and still not reduce back to approach speed by 1000 Rad Alt?
I find it hard to believe that with a headwind that this is so difficult to achieve.
I think this is a big part of the issue. I'm pretty sure all the types in BA can do this and on the odd occasion that it might be difficult (tailwinds, light weight, icing, etc.) a quick word to ATC before starting the approach and all is well.
I'll stick my neck out here and say that I've been operating into LHR for over a decade in large and small aircraft and have never really had a problem with this requirement. Sometimes I've had to use the gear, flap and (horror!) the speedbrakes but it wasn't what I would term "rocket science".