When an area is dimensioned, all the ‘dwellings’ that are appropriately registered as a ‘proper’ address are in effect counted and number used to provide the appropriate size of the network for that immediate area , so your problems are two fold , first you would have to get the studio it’s own postal address , ( otherwise it would never appear as an valid address in the systems used to raise an order ) by making it a property liable for council tax etc , then , once the property is registered an order potentially could be raised , provided there was spare capacity at the CBT , capacity is probably OK , but there is a chance of no spare ‘fibres’ at the CBT
As already suggested the most obvious solution is your own Ethernet ‘cable’ between the two points , or even a point to point microwave link , if there is line of sight , and the prospect of providing a cable link is not practical,
FWIW, you don’t need to adhere to the same standard as Openreach would ( putting cables underground at the appropriate depth of cover , reinstatement etc ) so for arguments sake an Ethernet cable laid overground ( possibly in some sort of flexible conduit) between your house and studio would be no one’s responsibility but your own , if it were damaged , tripped over , etc
