My 200l Vaillant DHW tank falls from 70 to 65 (immediately following a legionella cycle) in about 11 hrs, just shy of 0.5C/hr.  Yours is quite a lot faster even at the lower temperature.

My tank is well insulated but the surrounding pipework not at all (at our request - the lost heat is useful in for us to create an airing cupboard).  

Is it possible that the diverter valve is not fully switching over so you are pumping cool water through the DHW tank?  Another alternative is that your DHW cycle isnt long enough fully to heat the tank, so the sensor is recording a faster than actual cooling because the transition between hot and cold is 'passing' the sensor.  It seems like there is a stepwise change in gradient at 50C in one of your plots, whereas you would expect the gradient smoothly to decrease.

From what you say Im assuming the buffer tank is separate, its temperature should (probably) only affect the DHW if there is a fault in the diverter valve.

The amount it can drop before it reheats (10C you say in your case) is usually called the 'hysteresis'.  Its probably adjustable somewhere in the installer settings.  However if DHW is 'timed' the logic may cause reheat to start only if (DHW temp<set DHW temp- DHW hysterisis AND time is within the set DHW operation window).  Certainly thats how my Vaillant operates.  Mine was set to 10 and, because I reheat daily to 48C, thats far too high.  I have it at 5 and may even reduce it to 3.  Obviously a low hysteresis isnt a good idea if you have the system set to give priority to DHW, but if you are doing timed DHW it makes more sense to set it low.

@jamespa Thanks for the information. I found the hysterisis and in my case it is 8c, I was considering changing to 5c, but I really don't want to change it to work around the "problem" i have raised a case with Octopus. I can hear water running in the tank in the loft. My Mum has the same system, but her tank is in the old airing cupboard. I can not hear water on her system. The issue has only be noticeable recently and I am wondering if that is due to the outside water being colder and making the issue worse. I will update this when Octopus have looked at it.

Posted by: @bazcurtis

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I found the hysterisis and in my case it is 8c, I was considering changing to 5c, but I really don't want to change it to work around the "problem"

Agree.  I changed mine because I reheat only once per day, which is fine so long as hysterisis set too high cause it to skip a cycle.  However you seem to have some excess loss so as you say a different issue.

Somewhere you should be able to find the spec for the loss of the DHW tank, which should in turn allow you to calculate expected temp drop.

This is what I can see in the attic:

All of these brass fittings need insulation.

Even for a tank within the thermal envelope of the house, you would expect to have all metalwork insulated within 1m of the tank wall.
Otherwise the copper pipe draws heat out of the main body of water.

The pipework which gets most frequently overlooked is the pressure-release valve and the descending pipe to the tundish.
Just because it doesn't contain water won't prevent it from draining heat.

The sound of running water indicates that there's air in the system.

I can see one air-relief valve to the left of the tank.
I assume there's another one at the top of the vertical pipe at the top of the tank, close to the ridge board.

You are correct in what you seek: "The sound of silence"

Finally, is the weight of that tank and surrounding pipework entirely supported on that sheet of plywood?
Its mass will be almost a tonne.

I don't like the look of those fixings into a single pair of rafters.

What's the thickness of the board, and the size of those screws/bolts?

Posted by: @transparent

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Finally, is the weight of that tank and surrounding pipework entirely supported on that sheet of plywood?
Its mass will be almost a tonne

Are you saying that tank weighs a tonne? The tank isn't that large, it is 26 litres. I think it is buffer tank. Thanks for the insulation information, I will get that sorted. Would air in the system cause temperature loss?

Ah... I didn't get the sense of proportion from the photo!

Rough rule of thumb for mass of tank is
1Kg per litre of water...
... but that stated capacity may not include the volume of water within the heating coil (in the case of a DHW tank), so add that separately

Then double that figure to account for the tank materials themselves and attached pipework.

I can't see how air in the system would account for heat loss by itself.

But air expands when it gets warm, which increases the pressure of the system.
That might affect the modulation of the pump.
It's the pressure difference across it which changes the speed at which it runs.

So the presence of air can alter other parameters which the ASHP needs to operate effectively.

I think I might have cracked it. I checked the pressure in the system and it was zero. I have put it back to 1.5 bar and the water sound has stopped. I need to monitor the temperature today. I will report back. I have written an automation in Home Assistant to warn me if the pressure goes below 1.

Great!

Keep checking the pressure. If it increases when the system is warm, and reduces when colder, then you have air in the system.

If it slowly falls over several hours, then you have a weeping leak somewhere...
... usually concealed beneath insulation in a dark corner!

If there's a leak in the attic space, then beware that it might've been due to an overnight frost causing ice.

My call-out fee for the next couple of days is £250/hour plus travel 😉 

And yes, I did actually spend Christmas night repairing a leak in a neighbour's attic pipework about 10-years ago.
They lost all of the ceiling in one room, and partially in the next room.

If you don't have any emergency leak-repair tape (self-amalgamating rubber), then now would be a great time to treat yourself to an early Christmas present!

@transparent Thanks for the advice. This is what we have seen today. The tank temperature looks much better.