Have read plenty of heater threads from various forums, but still not quite sure I know what to do next.
I appear to have two separate heater issues.. I think unrelated.

On manual, the heater fan works at all speeds. If you turn the heater temperature control knob all the way down to the coldest setting and select auto, it selects a high(ish) fan speed until the car gets cold, which is the expected behaviour… but turning the temperature control to max, the fan speed stays low.
Annoying, but I can probably live with it.

The more serious issue is that the heater matrix on both sides doesn’t seem to get hot unless the engine revs are at 2-3k.. at 3k the heater blows really hot air on both sides, back at normal rpm (sub 1500) the heater blows cold.

I’ve only had the car a few weeks, so not sure exactly what’s happened to it. Before I owned it, the oil cooler leaked in the usual way.. this has been fixed, but the cooling system still hasn’t been flushed properly. I recently dropped the coolant out again, and replaced the single heater valve on the drivers side inner wing. This hasn’t helped, but understand these are a common failure so I replaced it anyway. Coolant is now cleaner but still not clean.

I can hear the aux water pump run with the ignition on, and can hear some gurgling noises, but suspect there may be an air lock… but I purged the air out of the heater matrix with a hose pipe, so hoping that’s now been cleared. I’d have thought me driving in low gear at high revs for several minutes would have cleared any remaining air, as the heater got hot.
The diverter flaps seem to be moving ok when the temp is changed

So what do I look at next? I’m tempted to change the twin valve on the left hand inner wing that sends water to the two heater matrix’s but as both left and right are behaving the same, it seems unlikely. Could it be the aux pump? Or is it just that the system needs to be cleaned properly from the oil contamination? Some of these parts look to be a pain to change, so want to try and minimise further work until my diagnostics are more convincing.

Any thoughts about my next move?

To me, that sounds like air in the system. I don't know the TDV8 but I use a vacuum device on my 5.0SC, without a vacuum it is almost impossible to completely bleed the system. If you hear a gurgling sound, it is very likely that air is still "trapped".

Well I bought a vacuum filling and pressure testing kit. Put some coolant flush in,Drained the coolant and vacuum filled it. Still the same… I then pressurised the system and loosened the heater hoses to purge out any remaining trapped air… still the same.
I can only assume this isn’t an air lock, so going back to the theory of it being the electric coolant pump.

I had this same issue several years ago on my 2005 4.4 Petrol V8. I discovered that the V8 does not poses particularly good coolant circulation to externals like heater matrix at low revs so they installed an auxiliary heater pump on the left hand bulkhead below the two heater control solenoids, Pretty much directly below the suspension top turret. Not too bad to access if you take both heater controllers out with the pump. I replaced my pump and it's been much better ever since (6 Years or so) although I do still notice a heater boost in winter after an aggressive acceleration but the car heats up fine even at idle.