Take up the Hold/Rolaaand
Unless I specify a speed to an a/c within first contact, they will (85% of the time), come back and ask. That in itself is a little annoying as my answer will invariably be "fly standard/normal speeds". Annoying because of course that is what they should do unless instructed otherwise - it's a transmission I should not have to make.
Once given a speed, they obey it - having Mode S helps!!
As for the difference between our TMAs - yes the LTMA might be more packed more often, but they are both, by their very existence, extremely complex bits of airspace. I would hope that pilots did not think that just because they expect it to be quieter, they can disobey your instructions.
We very often get A/C from LACC on speeds anyways - usually 300kts or greater, so when the pilot reports that, we will invariable give an instructiuon regarding speed.
DFC
As for explaining why you are put on a heading - if (and I purely speak from an LTMA perspective here as I do not have knowledge of other places) I was to explain every time why I took you off a SID or turned you left when running into the fix etc, I would not get anything done.
In TMAs although there are set routes, the very nature of the job (multiple crossing tracks with A/C needing to climb and descend) means that we will need headings to get A/C moving.
If I turn an A/C 20 degrees left as it runs into Biggin so that I can climb an A/C outbound from EGLL or EGKK (which wil also be on a heading) it is done with the best interests of all A/C involved - it means I can give the inbound A/C a descent as well. It means that the outbound A/C are not left at lower levels and the inbound A/C are not too high at the holding point to come straight off. I would say that 90% of A/C in the LTMA are on headings.
We are not going to tell them all the reason why!!
There are far too many tactical reasons that we use headings for us to have the time to explain it. In an ideal world, we would, but it is far from ideal!! The most a pilot would get from me is an assurance that there would be no delay due to my vectoring; and then only when I have the time.
You may be put on a heading to take you away from an A/C that is working a different controller using shared airspace. That A/C may not even be on frequency yet but we know its coming from our forward planning.
When you are flying airways and taken off a route, then yes, maybe you could expect a bit of an explanation, but please bear in mind the complexity of UK and other airspace.