I posted this request for help a while back, under my old profile (which I never could re-enable so I'm back under this one).
It had some other things to check.
http://www.triumphrat.net/showthread.php?t=45938
For my part, I've replaced:- both tyres, had the seat recovered, new handlebars (they were bent, about 2" out of true on the right hand side), steering head bearings replaced, forks serviced, alignment checked on frame and wheels and I still get the steer right problem though admittedly a lot less than before
Yes, it's definitely worse on a road with a camber that leans right, and there are a lot of dual lane roads round here that dip to the central reservation to spill water when it rains. It's almost un-noticeable when accelerating, but at steady 55, 60 mph speeds it does have a distinct drift right.
Next up is to check the rear shock, so it's out with the trolley jack at sme point. I have noticed I tend to slide to the left on the seat, though less so now with the new tighter cover. I was theorising that this was upsetting the centre of mass and to counter this I was leaning the bike right, thus sending it into a gentle turn. It's all very strange and not at all fun, to be honest it's spoilt what little decent riding I have been able to do this year.
I'm also going to try and get a test ride on another bike, it may after all this be down to me.
Almost forgot, the bike also pulls right when braking, but it's always done that even prior to the right steering tendency. Oddly, another quirk is it is much easier to take a right hander than a left. But that doesn't seem uncommon and could have many explanations other than a bike one.