Bookworm
UK controllers should never tell you to
maintain a heading, that's reserved for level instructions. We might tell you to
continue on a heading however
Personally I never ask an aircraft what his heading is before adjusting it, with one exception. It's 4 RT calls when 2 will suffice. Why double your workload in busy airspace ?? I can see from radar the track of the aircraft, I know how many degrees I want that to change the track by and can factor in the approximate drift, and I can ask the pilot to tell me the new heading if I really need to know it. If it's to find the 'heading du jour' then again I will tell the pilot to continue on the heading and report it. Again, 2 RT calls instead of 4. The only exception I would make would be when using the turn method to identify a non squawking aircraft since I need to know his heading to correlate it with the radar return I think is the aircraft in question before issuing the ident turn.
3 "Turn left 30 degrees and report your heading"
Probably still maintain a heading mode, but less obvious, I think.
There is a slight disconnect here between the MATS Part 1 (ATC) and the CAP413 (Pilots/ATC). The MATS permits this phrase as a means of vectoring aircraft, therefore in ATC minds it is a 'continue' heading mode. It doesn't seem to appear in the CAP413 in this format, so I can see where the confusion arises.
5 "Route direct XYZ"
Still probably own navigation, yes?
Yes
6 "Route direct XYZ and report your heading"
Er. Well by analogy with 3 we're in maintain a heading mode. By analogy with 5 we're in own navigation mode.
Non standard phraseolgy (by mixing two differing types of instrucion) which will always cause ambiuguity and confusion. If I want someone to route direct somewhere but then need them on a heading for separation because I don't have the requisite number of miles to allow me to simply monitor the separation (differs depending on the RNP status of the airspace, see previous lengthy threads

), then I would say 'Route direct XYZ, when established on track continue on your heading, report heading when steady'. It doesn't appear in the list of standard phrases but hopefully is clear enough.
Gonzo
It puzzles me that some crews believe being told to 'report your heading' is equivalent to being told to fly/continue/maintain your heading'.
I think this comes from the CAP413. The paragraph header for vectoring states 'It may be necessary for a controller to know the heading of an aircraft as separation can often be established by instructing an aircraft to continue on its existing heading.'
One of the standard phraseology 'instructions' given is then 'Fastair 345 report heading'. Reading that as a pilot I would think that it infers I must continue on that heading so the controller can establish separation. As an ATCO, I wouldn't expect them to, but clearly it is ambiguous.
I think I'll serve this one to an SRG inspector and see if we can have it sorted once and for all