I've always found there to be very restricted space between the top of the carb and the bottom of the tank, on all my Ariel singles.
I have to avoid using adjusters at the carb end and get the cable outer sitting as low as possible by using cables with a 'middle' adjuster that have the ferrule at the carb end like an upside-down top hat that fits down inside the carb top. You can see the difference in the cables on Draqs' web-site:https://www.draganfly.co.uk/index.php/a ... 727-cables
Trying to think back a long time to when I had a 276 on an NH I think I might also have been able to use a 'standard' cable but with a split ferrule (like the one used at the throttle twist grip but smaller) that let the cable outer sit level with the carb top - this would be a bit like Luiz's throttle cable (in the pic) with the lock nut taken off and the adjuster screwed fully down.
'55 Huntmaster, '56 VH, ' 51 VH, '80 R100RT, '00 Sprint ST (but all those Ariel parts can only make one running bike...)