For home use, does the running bush need to be hardened, or would an unhardened mild steel bush do the job for the limited hours of use per year it will get, running in the bronze bush?
Or maybe use something like SAE 4140 high-carbon alloy steel? (No idea what that is in UK grading system.)
If you do turn the original hardened bush down, you might need to grind the final finish on it to get a smooth bearing surface? Whereas, turning up a fresh unhardened bush, a bit of emery paper will give final finish?