Hi Sean. It's always been not below 4000' till 13dme on 27.
Sometimes if there is nothing about (city departure) we might cheat and drop you to 3000 early particularly if you're still descending and present rate makes it unlikely you will get below 4000 till 13 dme. This is a little corner that is cut to manage the RT more effectively but is not strictly by the book.
A big disadvantage to using that technique is you guys start to expect it and then start asking for lower thereby blocking the RT at a critical time. (sounds like that's what happened to you?)
Next time you're in that position it would be nice to take you downwind an extra mile to make sure you hit the LOC outside 13dme but you'll be going round and round at LAM even more than you do now if that becomes the norm. Likewise, I'm sure the controller in question wanted to descend you at 13dme but at that exact time he/she had a higher priority call eg. a turn or speed reduction to ensure the landing rate.
Unfortunately LL is at such a high capacity and so constained by airspace that sometimes you and I have to work at lot harder than we'd both like in order to keep your airline and my bosses happy.
Out of interest, what do you fly and what do you consider to be the optimum length final into Heathrow?
Also, if you are in that position again would a descent to 2000/2500 then further with the glide enable you to capture from below or is it better (though not ideal) to capture from above?
I'd like to think that my colleagues would recognise you were high on the glide at any stage of approach and expect a subsequent speed reduction to take longer than usual.