Hello Melon, I will give this a go for you as no one has responded yet.

I've gone through multiple rounds of balancing with the installer (no temp measurement, just guessing), and various other tweaks to the system.  All the lock shields upstairs were turned right down to try and encourage more heat to go to the downstairs radiators. The radiators at the end of the loop downstairs are fully open. All the radiators are new and the systems been flushed, so I ruled out any kind of sludge or blockage.

You must balance the emitters using balancing equipment such as meters able to read either flow or DT. IR cameras help as well.

My feeling is that the flow rate is not high enough to deliver the required heat to the radiators downstairs. 

This could be that the index circuit is suffering if this happens to be the downstairs circuit (your installer will be able to show you some great Math to indicate the index circuit and emitter) The flow rate could be high enough but all being sent round the emitters upstairs, equally it could also be bypassed, stalled or restricted at the branch.

In response, the installers have claimed the following:

- Heat rises so downstairs will be cooler than upstairs  

Hmmm, ok but not if you balance the system and reverse this, thats the point of balancing and designing the correct emitters to come with different loads in each room as well as rising heat.

- Heat rises so it's normal for the bottom of the radiator to be cooler

Fractionally yes but maybe a deg, heat convects so eventually the radiator will be hot all over assuming you are running the system at a high enough temp (at least 10 deg over room temp desired.

- Flow rate through plastic is better than copper as the pipes are "slippier"

This may be true by 1% more efficient but this is only if you are comparing straight pipe for long lengths, connecting bends are more restrictive in push fit plastic than soldered copper on equal sizes. This argument would only stand up in comparative circuits and you design to overcome these it is not something we accept, if the pipework is wrong change it to make the emitters downstairs to works then.

- Flow rate reported by the heatpump is good (~ 22 litres per minute), so it's not an issue.

I assume that it is a 7.6kW system running at that rate and that equals your heat loss for the whole house and the heat loss for each and every room has been carefully balanced to match each room?

Despite their assurances that there isn't a flow rate issue (along with some very questionable information),  I'd already lost trust in their competence and expertise. 

No comment.

I'm hoping the members of this forum who are much more knowledgeable and experienced than myself, might be able to confirm/reject my assumption, and the rebuttal I've received from the installers. I've attached a rough approximation of the pipework for the central heating (DHW omitted) to try and clarify things.

Its quite hard to tell everything from a basic schematic and limited info but there may be a couple of things you can try and with the power of deduction we may be able to help steer you in the right direction. Do you have TRVs on any of the rads? if you do, close of every room apart from the down stairs rads and confirm the flow rate at that point and if the ground floor improved. 

- Assuming the heat loss is correct, is flow rate a likely cause for the temperature difference?

We can try some things to rule this in our out

- What sort of temperatures should I see between the top and bottom of the radiator, I assume it should be less than or equal to the delta T?

Half the temp rate left to right but up and down need to be inline so something like this: 45 flow 40 return = Centre of rad 42.5 /  43 Av bottom of rad 45 Av top of rad av rad temp (ultimately they could use a thermal camera and you will see bottom is 43 top is 45 ish) The point is not much of a difference that you could tell with your hand by touch.

- Given that the flow and return T off to serve downstairs, is it possible that the flow rates downstairs will be worse than upstairs? Is the flow rate reported by the heat pump telling the whole story? 

No the flow rate on the heat pump is only at one point in the circuit and gives a very good indication only, so you may see that most of the flow can whizz round upstairs starving some of downstairs, watch out for bypasses they do the same thing. A good commissioning team will use DT equipment and iR cameras to check flow to every emitter.

The old boiler was downstairs, and I never noticed any issues with temperature between the two floors. 

unfortunately comparing the old boiler to new installation would be misleading, one system was high temp heating and the new is low temp heating they are not designed the same which seems to be the fall down with commissioning.

Can you try the following to rule some things out: 

close all of upstairs TRV's if you have them and run the system, see if the downstairs rads improve and check the flow rate at this point and report back to me.

Hi Bobba, thank you so much for the considered and detailed response.

We have TRVs installed on all the radiators, aside from the bathroom with traditional valves, and a bypass radiator on the landing. So far the TRVs have been left fully open downstairs, and turned down upstairs in the bedrooms to try and keep the rooms cooler. 

I will turn all the TRVs off upstairs as advised, set the flow temp to 45 (turning off weather comp), and report back. Fortunately it is a little colder today. 

For extra context, we have an 8kW Daikin Monobloc 3, for a 6.3 kW heat loss.