If the inverter is sensible and knows the difference between charging a battery and exporting to the grid (i.e. as has already been mentioned, the battery is fed directly by the inverfter and does touch the house wiring) then it should charge at whatever rate it can - the limitation is on exported power, for reasons of grid stability.
Understand, thanks.
When you look at your solar graph, you will probably see (as mine does) that you get a sudden switch on of solar export, that is happening when the battery is full, before that moment, the inverter is loading the battery.
Wee update… Installer is coming back out to put in a 6kW inverter which we should have had along and submitting the DNO paperwork