When the bit broke off, it must have left a burr inside the tube, along with a slightly misshapen bit end. By careful filing inside the tube, and gentle persuasion with a centre punch, it eventually took flight - I've yet to find it in the workshop!
Considered superglue, but there was a lot of oil/grease around that couldn't be dispersed. Also considered welding a welding rod to it, to pull it through. That worked a long time ago on a broken half-shaft stuck in its housing. Trouble with that is it's a one shot only. Touch the side of the tube instead of the offending bit, and it's all scrap.
Thank you for the answers, cost me three hours trying, but it's pride that counts! Besides, drills don't do much for landfill...