Before reaming out the bore of the gear-wheel…..
Have you abraded the replacement axle where the gear wheel sits? This replicates the knurled axle used by Hornby. Lay the axle on a cutting mat or similar. Take a coarse file and applying pressure, use the file edge to roll the axle up and down the mat. Try and limit the abrasion to the gear wheel position so take care.
If you twisted the gear-wheel off the Hornby axle instead of sliding it off, you may have damaged the gear bore. This might explain why you have a loose fit with the new axle. In this situation there is a chance that opening the gear bore out may not work satisfactorily. I suspect it may be better to buy a replacement gear wheel from Peter’s Spares.