Hi mate,
I'm a plumber. If it were me I would buy a new tap. The backplate which is secured on the wall will 100% have a 1/2" BSP thread.
You'll need: A new tap, a roll of PTFE tap, a big spanner or pair of grips.
Turn water off.
Run tap until it stops.
Grab hold of the tap with spanner/grip and turn anticlockwise being carefull not to stress the adjoining pipework.
Remove tap.
Wrap PTFE around new tap thread CLOCKWISE approx 12 wraps (very important) trying to keep it reletively tight.
Run new tap onto the existing threaded back plate.
Tighten by hand, if need's be use grips to tighten, hardest part is trying to get the tap straight but tight enough, may take a few goes.
Makes sure tap is off and slowly turn water on check for leaks etc.
Must admit i've never seen an issue with those hosetail adaptors, maybe the thread is damaged although it looks fine, even so save messing around and change the tap IMO
HTH Sam