Heat Geeks have recently brought out a new range of tanks for this type of situation. I will look up a link later and try to post it here but, basically they have designed a smaller tank that is capable of fast reheat times. Adam Chapman is behind the design and another company manufaactures and sells them. In the meantime, you may care to search for Heat Geek Hot Water Tank. Regards, Toodles.

This link will take you to a Youtube presentation by Adam Chapman - worth a consideration perhaps? @zuluwarrior 

Should you wish to know about another method of heat battery, look at the Sunamp range; their unit are approx. 25% the volume and are electric and heat pump powered.

Regards, Toodles.

I've just checked in my Vaillant app and see that I can set my Arotherm to heat the hot water up to 70C which is higher than you are envisaging. The downside is that the heating efficiency will drop but still be a lot better than using an immersion heater.  A further measure you could take is to set the hot water schedule to (i) get the tank up to temperature in the night when the heating being off won't be noticed followed by (ii) another heating period just after the shower usage has started (if need be this can be scheduled to be different between weekdays and weekends) to put some more heat into the cylinder to offset what is being taken out. You wll probably find that you can have a lower target cylinder temperature in the summer when the incoming cold water is warmer.

Welcome to the forum!

Posted by: @zuluwarrior

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My partner thinks we could run the Arotherm at 65 degrees or more

This is getting too hot - you might end up cooking one of the nippers (if they are nippers). The showers might be OK - until the mixer fails. The water coming out of hot water taps will be hot enough to scald in seconds. And there are the efficiency penalties.

This is not really what heat pumps are designed for, ie a lot of DHW with a bit of space heating on the side. It defeats the low and steady way of running heat pumps. Given your limited tank space, you can't semi-solve the problem by having a second 300L tank (or perhaps you can? Certainly worth thinking about). One of the Heat Geek solutions might be an option. But overall I think you are close to trying to fit a quart into a pint pot, or more accurately eight showers into too small a tank. It needs thinking about. There is a lot of expertise on this forum, I do hope for your sake someone comes up with some useful ideas. 

Posted by: @zuluwarrior

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As an average shower is 8 minutes. It would be roughly 4 showers but we need at least 6 and ideally 8 showers and the reheat time would be 100 mins.

We need to do some energy calculations!  Over what period do you need 8 showers and do you know the water flow rate even roughly.  We need these numbers to do the calcs.

You should also be asking yourself whether you could use water saving shower heads (which can halve water consumption for a similar 'feel') and whether you really need 8 minutes per shower.  8 showers at 8 minutes per shower at 20l/min (which is not uncommon, although it is unnecessary) equals 1280l.  That's needs 44kWh which is a lot of energy, even for a big gas boiler, and also for the coil in the tank.  If you were to do this every day it will cost £1,300 per annum whether heated by gas or heat pump.  

@jamespa We are thinking that ideally 6 showers could be had in the morning but were calculating based on a flow rate of between 8 and 10litres per minute

@cathoderay We were more thinking the very hot water would be mixed with cold water to create shower hot temperature i.e. around 40 degrees

Posted by: @zuluwarrior

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We were more thinking the very hot water would be mixed with cold water to create shower hot temperature i.e. around 40 degrees

Yes that can be done, but why do it? If you want a pint jug of water at 40 degrees C, there's no need to boil a kettle, and then dilute the 100 degrees C water to get 40 degrees C... maybe it is to get the volume? But the risk of scalding still remains if something malfunctions or human error kicks in. 

Hey, similar situation to myself. I’m in a new build with a Vaillant 7Kw. Rads up stairs and ufh downstairs. When up stairs wants demand downstairs struggles, but back to the hot water. We came home the other night and basically had a shower one after each other but by fluke, nearly 50 mins apart. So I used then son, etc etc. but after I used it, the heating stops to heat just hot water. So my heating was off for hours. Is this normal. Do all heat pumps only do one or the other. In the morning, if we have showers, similar situation. Feel like I need one for dhw and one for heating. Madness really. And yes, 300 litres is nothing, we are real world usage ha ha , 10 min showers. Vaillant said the average usages for one person in a day is 50 litres per person. A tap is 5.7 litres a min. Ha ha. Wild. 

Posted by: @tomhartley

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Do all heat pumps only do one or the other.

Any heating set up with either variable or low flow temperature does this.  In the UK we normally set up boilers to run at a high fixed flow temperature.  As a consequence they can do both at once, but the penalty is that we are (in most cases) paying ~10% more for our space heating than we need to and enjoy a lower standard of comfort!  Some other countries set boilers up to run with much like heat pumps, with variable and lower flow temperature.  This reduces cost and increases comfort, but the penalty is that only DHW or space heating can be active at any one time. 

In Germany, for example, this set up has been mandatory for many years.  Our building regulations now also specify a max space heating flow temperature of 55C which is insufficient (or at best marginal) to heat DHW so we are going in this direction.  

If you need a boost you can use the immersion - the additional cost is much less than the extra cost would be if you ran at a fixed, higher temperature.  Depending on your system you can also schedule multiple, shorter, DHW reheats during the day/night

Unfortunately there is no perfect heating set up, or if there is nobody has yet discovered it!

Posted by: @zuluwarrior

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@jamespa We are thinking that ideally 6 showers could be had in the morning but were calculating based on a flow rate of between 8 and 10litres per minute

OK lets go with 6, 8 minute showers at 10l/min.  So you need 480l of water at 40C.  If you start of with 300l at 48C (a common setting) and mix it with incoming mains at 10C, you will get 380l of shower water from your 300l tank.  Thats already enough for four and a bit showers.  You need to make up a further 100l for the remaining ones.

The energy required to heat this from 10 to 40C is (deltaT* specific heat capacity of water * volume) = 30*4200*100J = 12.6MJ = 3.5kWh, which a 7kW heater can supply in 30mins.  Thus being the case provided 

a) you start with a full tank

b) your tank is well stratified (the hot water is at the top) - which a modern tank should be

c) you reheat while showering

You should be able to generate enough water in the time, albeit only just.  

This being the case it may be sensible for you to think a bit about the options, rather than oversizing the heat pump.  They include

• Flick on the immersion heater in addition to the heat pump while reheating during showering, giving you 10kW total
• Heat your DHW to 58C which will give you sufficient without reheat, accepting this will cost a bit more
• Reduce shower flow rate to 8l/min
• Reduce shower time to 6 minutes
• A combination of the above
• If you have space, get a 400l tank

I think that, with a bit of thought, this problem is soluble without compromising your choice of ASHP. 

And, if I may say so without causing offence, please bear in mind that this is very much a 'first world' problem!