That made me think the problem could be with the bottling process, rather than with the fermenter etc.
I dismantle my taps and thoroughly clean and sanitise them before storing, as I do my fermenters, and sanitise again before each brew, and before each bottling session, so I don't think I have an issue there.
As I was getting ready to bottle today, I had a close look at the little bottler end, and realised there is a small rubber washer at the end of it. To my surprise, it was gunked up with old beer / yeast / hop etc residue, despite my thinking I had cleaned it each use.
I have now dismantled it, cleaned it, and sanitised it, so I am hopeful it will solve my problem.
For those interested, here are two pics, one with the washer in place, and one with it removed.
Edit: better pics

