There are some really interesting answers here, and I thank you all for taking the time to respond. I hadn't realised that a good few others are in a similar situation.
I had Gartorskins on as I thought that these were a good combination of low rolling resistance and puncture protection. Looking at the table Samuel D linked to, I see they are way down. I have a pair of Vitoria Rubino Control tyres which are better. However, I do have a pair of GP 4000's on the Canyon so I may just take them off to try and see what the difference is.
Continental Gatorskin 19.3 W
Vittoria Rubino Pro Control 16.9 W
Continental Grand Prix 4000S II 12.2 W
Wheels are the next thing if the tyres do not make an appreciable improvement. I have a pair of Campag Zonda's on the bike that's on the turbo (I know, too good, it's another story). They could come off for an experiment. Don't think I would use them for audax or touring as they do not look to be strong enough (I could be wrong). I have also been looking at lighter rims and 28 / 32 spokes instead of 36 built up with a dynamo. Maybe that's the way to go if the Zonda's are a revelation.
My other option, of course, is to sell the bike and get something else. Sorry Mattc, the lack of money was the clincher. I have been looking at steel frames and that remains an option either as a replacement frame or as a new bike. But lets try tyres and wheels first.