Upon a bit of further checking the energy grant may only cover heat pumps connected to the central heating system.
It's possible this is covered but the more I think about it, the more I think this may also not be the case.
Good news is that we've possibly more or less had the heat wave for this year now, so you've got time to get that figured out.
Does seem counter intuitive to get AC under a green grant, will make some enquiries next month, cheers