Yes correct. I’ve corrected my original post. This is the source I was reading: Do I Need Planning Permission For a Heat Pump? - Evergreen Energy.
I’m not an expert on planning rules, please do your own research!
This is the definitive answer referencing official documents:
Definitely shelving plans for an Eddi if Octopus continue to pay more for solar export than they charge for night rate. Just been switched from 4.1p/kWh to 15p/kWh!
I emailed Oxford City planning and they confirmed that an air to air unit which cools as well as heating would require planning permission. The duty office then couldn’t say if having the gas boiler replaced with an ASHP after having the air con installed would be permitted development, as it might count as a second heat pump. 
Looks like I can knock another £2.5k off my expected costs thanks to the BUS news. Although it also makes me think that I might need to try to switch year earlier, as there doesn’t appear to be more funding, so what’s there might run out more quickly.
Get a cylinder rather than a Sunamp if efficiency / longevity are your objective. The Sunamp units are compact and avoid some of the discharge requirements but they compromise the efficiency of the heat pump and are costly.
I had a heat loss survey done last week, and it turns out that I can get away with a 3.5kW Vaillant. Probably only space for a 120L, maybe 130L, tank in the cupboard, but as it’s usually just me that should be fine. Looking to get a green 0% mortgage to fund both the heatpump and some extra battery storage being installed in the summer.
Also following the proposed changes to permitted development with interest, as it seems for detached properties it might be possible to have two heat pumps, and there’s also a suggestion to allow air to air that cools, so that would be sorted for some aircon too.
Thanks again to everyone who gave me feedback.
I already had two outdoor air-to-air units when I got my ASHP quote from Octopus. They required planning permission before proceeding so I applied for pre-planning advice before full planning permission and was told that the ASHP would still fall within permitted development. The document they sent me confirming this said
The existing air conditioning units at the proposed site would not affect the permitted
development rights in regards to the air source heat pump. As the air source heat pump would be
considered under Schedule 2, Part 14, Class G of the Town and Country Planning (General
Permitted Development) (England) Order 2015, as amended, the air conditioning units fall outside
of this section of General permitted development.
I’m in Newark & Sherwood so obviously depends on the council but the pre-planning advice was only £70 instead of the full payment.