Welcome to the forum.

Can I ask a few basic questions to help diagnose.

Aside from 'my scop isn't great' what exact  problem are you experiencing with the heating.  Is it just " in the coldest of days in the first 2 winters the unit has struggled to heat the house adequately" or is there anything else.  You mention two rooms specifically, why did you single those out?  How many 'coldest days'?

What scop do you get?  

Are you operating weather compensation and if so what are the settings.

How do you operate it 24*7 or timed

Do you have trvs or thermostats and if so how are these set?

Aside from JamesPa's comments and questions, quietly swapping a specified 11 kW unit for a 9 kW one, then updating the certificate months later, isn’t acceptable practice in any shape or form, not to mention that a 9kW is cheaper than an 11kW.

I agree with @editor, and would also suggest that it may be worth having a quick chat with the Citizen's Advice Bureau to see how feasible it might be even with this amount of elapsed time to put a claim into the small claims court for the monetary difference between the 9kW and 11kW unit especially, I might add, if the invoice says 11kW unit and the writing on the actual unit shows it to be a 9kW. Charging for one thing and fitting another is still against the law, after all.

@mairia, who was the installer? If you don't want to mention them publicly, feel free to email me (editor@renewableheatinghub.co.uk) and please send me their quote and/or invoice if you'd like for review. 

Frankly, I'm getting fed up with the number of recent cases I've seen where the original heat loss has been "lost". These MUST be submitted to MCS as per their processes, which again shows the ineptitude of the MCS "standards" and lack of enforcement.

Just to say I do agree with @editor and @majordennisbloodnok that specifying one model and supplying another is unacceptable but personally I wouldn't spend a lot of time pursuing this until I had nailed exactly what problem this was causing me, for the simple reason that they are bound to argue and you need to be able to deal with that. 

It's also quite possibly that a simple adjustment will fix the problem and you may wish to try that rather than (or before) putting yourself through a lot of hassle. Your post does suggest that is the case.

You will be in a much stronger position to take up the case if you can be precise about the problem, particularly since it sounds quite likely that the unit supplied may in fact have sufficient capacity notwithstanding that it may not have been the one quoted.

Posted by: @editor

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Frankly, I'm getting fed up with the number of recent cases I've seen where the original heat loss has been "lost". These MUST be submitted to MCS as per their processes, which again shows the ineptitude of the MCS "standards" and lack of enforcement

I agree, but at the same time it's encumbant on homeowners to keep documentation supplied in case of a later claim.  I'm not sure it's right to expect installers to produce evidence just so that a claim can be made against them.  I have heard it said, a bit in jest but I suspect with some truth, that legal cases are won by the person with the best filing system. 

I'm not defending an installer losing stuff , but we all know it happens and would be well advised to protect ourselves!

@jamespa thank you for replying so quickly. SCOP has been running around 2.7 for the past 10 months, the best it has been in the early days was 3.2, maybe just reflects weather conditions. I check my figures weekly using the MMI and keep a spreadsheet. I changed to controlling the system on leaving water temperature rather than room thermostat over the winter especially as I found that gives a much more even temperature. I have watched a lot of Heat Geek videos to try to inform myself. Lounge especially, but also the hall are the most obviously cool rooms. I took some screenshots last winter of the Madoka, the worst day I see is 18.9 degrees on the thermostat (in the lounge), outside temp 1 degree, LWT 50 degrees - so heat pump maybe performing ok? That's what started me thinking about radiator size. Another day themostat 19.7, outside 2 degrees, LWT 39 in spite of offsetting to +10. Probably like this on a small number of very cold days, but I was disappointed that the house was so cold. I will monitor it more closely this winter. Weather compensation settings are 50 degrees at -3, 25 degrees at 14. It runs 24/7 with a 3 degree setback overnight. I have tweaked these a little over time. I switch the space heating off over the summer. I have an open system downstairs, TRV's upstairs in the bedrooms and bathrooms. I hope that all makes sense, I've tried to inform myself as much as possible about ASHP, but I'm no expert.

@editor thank, it's good to have validation of how I feel, the installer was really downplaying my concerns.

That's a helpful reply thanks.  You may be able to rule out an undersized heat pump by turning up the LWT when it's coldest.  If that fixes it then undersized heat pump is not the problem.  Also the night time set back could usefully be switched off when it's coldest, this has to be compensated for during the day and if either rads or pump are marginal then that simply might not be possible even if the design is correct.  If you heat dhw during the day then that's another restriction on space heating in addition to the night time setback, so id swap this to night at least when it's coldest.

If you can extract info on heat supplied Vs oat then plotting this will give another view.

What do you mean by "Another day themostat 19.7, outside 2 degrees, LWT 39 in spite of offsetting to +10. ", in particular offsetting?  Are you saying let didn't get to temp?  If so that's an important observation.

Have you got any monitoring capabilities other than manual?

I think what I would probably do is put your installer on notice that you believe there is a problem either with the radiator sizing or the heat pump sizing and also with scop which you are likely to pursue, and then take comprehensive measurements through the winter to diagnose/prove.  

Finally if you wish to share the spreadsheet I can take a look in case something pops out.

@majordennisbloodnok The installer's reply to that query was "There is indeed a £97 difference between the two units. However, when we purchased your Heat Pump, it’s worth noting that Daikin had implemented a 4% price increase in April 2023, which coincided almost exactly with the time of your installation. We absorbed this increase on your behalf, meaning you were charged at the pre-increase rate, by us, despite the manufacturer’s new pricing coming into effect. This ensured your project costs remained consistent with our original quotation and avoided any additional charges passed on to you". This is one of my reasons for thinking a Subject Access Request is worthwhile.

@jamespa this is my thinking at the moment. I will be glad not to have to deal with the installer again!