Im a bit lost here , you say you want to replace the brass female that you have just linked to ?
So why order that with a 6mm tail , its not going to fit to the braided clear you have !
What i use is the 4 piece set that was linked above from screwfix , also gotten from wickes at £8.99 .
What does the other end of the braided hose connect to ......pump/Di ?