The microbore is either blocked or the system really unbalanced, some rads barely get warm.

I should get someone round to a proper look but now the warm homes low/no interest loans have been announced that makes me want to wait until the details are fleshed out on that. I can at least start looking into local heat geeks.

OK so about 110 sq m with cavity wall insulation a good level of loft insulation, double glazing but uninsulated floors.  'Feels' like 3-5kW or less.  My house, 7kW, needed 3100 kWh to heat it month to date (thats to house not from grid), yours is 1274kWh, suggesting yours is 2.8kW.

So I think we know your house loss is ~3-5kW probably towards the low end of that range.  So you are likely looking at say a 5kW heat pump (there arent many that are actually less and you probably want this for DHW) and 2kW or thereabouts per floor.  You may well need a volumiser to keep system volume up to reduce short cycling.

As to emitters, given the geometry you could possibly consider a single A2A on the landing, if you leave the bedroom doors open, plus something in the bathroom.  However it might be difficult to manage/unsatisfactory and, if it were my house I would want to speak to someone first who has actually tried this arrangement before departing from A2W.  Its just possible you wont need heating upstairs at all if you dont mind it fairly cool, but you have said you need cooling upstairs so something has to go there.  You could possibly run the experiment with no upstairs heating in your current setup, see how the rooms settle.

Downstairs I cant see A2A being a good fit, its just too segmented, although you might just possibly consider A2A in the 4 main rooms.  But it lends itself to A2W.  Conservatory a possible problem space depending on solar gain/insulation/shading.

I would say there is at least a reasonable chance that microbore would work.  In principle you can get 750W through microbore at 0.9m/s and DT5 which may be enough for every room.  It will depend on individual room calculations and plumbing geometry however and needs to be worked out properly.

Cooling - if you go A2A obvious, if A2W perhaps fancoils in living room and landing, although the microbore feeds may limit effect so if you could do a couple more that would be good.  No guarantee this will work well enough and certainly it wont be full aircon, just some light relief.  Is closing blinds/curtains on the south side an option?

Im sure others will have ideas.  Id probably do the calcs, see if I can get away with microbore and if so just upgrade rads, if not think more carefully about A2A, but this is just a gut reaction not one borne out of any experience except my own house and a couple of community centres (in which I did A2A - but these were a small number of large spaces).

Hope that helps at least a bit.

This is the layout. The garage is currently getting converted, so that has:
150mm PIR floor insulation.

The walls are brick, 70mm cavity (based on a bore hole for vent) with blown in cavity insulation that may be patchy, then block with dot and dab.

Suspended timber floor the rest of the house, uninsulated. 

Loft insulation is 270mm with the top 170mm being recent.

The bay window may not be insulated on the roof area.

Built in 1999.

Conservatory currently has no insulation but a lightweight solid roof, there is a door separating but is an internal door with glass. 

All main house windows are UPVC double glazed from 5 years ago, along with front door composite.

Last weeks gas consumption was 275.77kWh, this month to date 1274.37kWh. Cannot seem to find annual consumption in the app.

Also got a 1.5kw electric radiator in the conservatory.

Working from home so house always occupied. 2 adults + 2 kids. 

Cooling to the living room and upstairs hallway might be enough to make the summers more comfortable, currently lugging a portable AC up and down in the summer months.

Got 3.6kW solar + 3.6kW 14kWh battery

Rear of the house is 144 degrees and South Yorkshire area.

There's a Dakin multi plus, that seems to do hot water too but I don't know if that can be used to heat water for the hallways and bathroom radiators.

A2A is relatively uncommon (at present) in domestic scenarios in the UK although absolutely standard in the commercial world.  The two sectors (commercial/domestic) are almost completely separated at least at present.  There is of course a domestic aircon (AKA A2A) sector but it tends to be confined to high end properties.  The other issue is that multisplits can sometimes work out more expensive that one ODU per IDU, which is bizarre.

For that reason, and the position as regards the BUS grant (which may be changing/may have changed) very few domestic installers know much about A2A heating.

I would say that A2A is more suited to open plan layouts, where there are fewer separate spaces, and newbuild, where there is no existing pipework and the loss is very low.  For older/more divided houses where there is already a pipework infrastructure I would say A2W is likely the better bet at present.  However that's in part based on the familiarity with A2W in this country, rather than being an absolute.

I wouldn't rule out being able to reuse microbore (but neither would I rule it in!), it depends on the loss and geometry.  Some installers will, apparently, take one look and say 'rip it out'.  Others adopt a more considered approach and do the math (which is whats needed!).  T11 rads can easily be upgraded to T21/T22, so thats not a particular problem, but it all depends on the numbers!

If you tell us some basics about the house (room configuration, current annual fuel consumption, age and state of insulation and where and to what extent do you need cooling) some more specific suggestions (with rationale) might be forthcoming.

There's a Dakin multi plus, that seems to do hot water too but I don't know if that can be used to heat water for the hallways and bathroom radiators.

Are there not external units that can be used for A2W in the winter and also have a couple of AC indoor units? Seems a bit much to have 2 external units one for A2W and another for A2A for cooling

If you want A2W then you may want to consider fancoils or UFH either of which will do 'light cooling' (ie cooling where you keep the water above dew temp so you dont get excessive condensation on pipes).  Several report this works satisfactorily.  Make sure you get an A2W unit that supports colling, in principle they all do but some have it permanently disabled in the controller or, like Vaillant*, require a dongle 

I don't know if there is a multisplit with a water heat exchanger, I cant see why not because the ODUs for a split and for A2A are, so far as I know, identical.

* Vaillant's dongle, which is physically a 4K resistor in a bit of plastic about the size of a USB drive, is ~£500.  The identical Vaillant dongle to code for LPG rather than natural gas is £10.  Just saying of course!

Are there not external units that can be used for A2W in the winter and also have a couple of AC indoor units? Seems a bit much to have 2 external units one for A2W and another for A2A for cooling

Ok so average A2A is 90w/m2 this covers as follows:

Standard 1950-1990 house 

South Facing rooms ground floor: 95-105 (assume windows are 1.5 x 1m and normal ventilation)

North facing rooms ground floor: 72-95 (assume windows are 1.5 x 1m and normal ventilation)

South Facing rooms 1st floor: 98-110 (assume windows are 1.5 x 1m and normal ventilation)

North facing rooms 1st floor: 76-98 (assume windows are 1.5 x 1m and normal ventilation)

Standard 1990 - 2020 house 

South Facing rooms ground floor: 90-98 (assume windows are 1.5 x 1m and normal ventilation)

North facing rooms ground floor: 70-90(assume windows are 1.5 x 1m and normal ventilation)

South Facing rooms 1st floor: 92-102 (assume windows are 1.5 x 1m and normal ventilation)

North facing rooms 1st floor: 76-85 (assume windows are 1.5 x 1m and normal ventilation)

Heating these room would be around 40% lower per m/2 

the above are based on a broad mix of heat loss calculations acorss multiple buildings and multiple ages, correct heat losses will tell you room by room but as you can only purchase for example 2kW, 2.5kW 3kW 3.5kW, 4kW, 5kW, 6kW, 7kW units for each room then even if you heat loss for the bedroom was 4mx 3m x 95w/m2 =1140 they would still select 2kw unit.

I hope this helps a bit. 

I have solar + battery already but a heat pump will be a hard sell to my wife so it has to go well when the time comes.

My house is a 1998 with 10mm copper mircobore with some 10mm plastic too, so really not ideal for A2W. Rads are mostly type 11 too.