Do I need to reuse these radiator connectors, or should I get new ones?
what should I ask for if so?


Radiator valve tails


  I can't see where to get a good grip


Use a large allen key (hex key) inserted into the bore. Probably 12.7mm (½") "radiator key" / "radiator spanner"

Workarounds include


Use a smaller allen key wedged in with a flat screwdriver
Attach an old/spare radiator valve, tighten the nut and turn the valve to unscrew the tail.



  whatever measurements I need


I surmise they're standard across the UK. My habit is to take the old parts to the store when buying replacements. A specialist plumbers supply store will have someone knowledgable behind the counter. Last time I did something like this (but not this), I walked in, silently plonked the old part on the counter, almost before it hit the counter the bloke behind it casually reached under the counter and then placed an exact replacement part on the counter next to mine and told me the price.



Source: How to Install a Radiator