that tap I used it on was 1/2" whitworth
Must have taken a bit of effort to break that !
The stores at Broadbents used to keep Walton tap extractors, which have extendable fingers to engage with the flutes rather than the machined ends of your set. The fingers can be obtained separately for replacement if they get damaged.
I think I still have some somewhere in the garage, but only in smaller sizes. It took me a while to learn to stop breaking 2BA taps when fitting switchplates …
Nigel B.