No, 0.75 only carries 6A so that will have to be replaced.
First, confirm that the switch is on a socket circuit or something appropriately sized. It is unlikely but it may have been taken from a lighting circuit or something that isn’t suitable for an outside socket.
Find out which mcb in the consumer unit it’s powered from. Should be 16A minimum.
The cable may be able to be pulled through the wall by attaching a piece of 1.5 or 2.5 FTE (flat cable) with electrical tape.
The fuse in the FCU is likely to be only 3A so that will need to be changed to a 13A, Alternatively, my preference would be use 2.5mm cable and then ditch the FCU as that will allow you to use both sockets to 13A per side rather than 13A total. Probably won’t ever need to but may as well do it properly whilst you’ve got the chance.
Rich.