It is not a problem Eddy as you can tie in any wayward shoots to your side of the trellis. When you cut them back in Spring you make your cuts as mentioned before and then just drag all the unneeded growth away. You can be quite brutal as it doesn't matter. I grow my clematises on an east facing garage wall with rebar as the support. I've just pruned them today and yanked all the unwanted stuff away.
Cacoethes: An irresistible urge to do something inadvisable
Eddy, if you are new to clematis I would advise starting with a Group 3 Polish Spirit, easy to grow, easy to prune, dirt cheap and a fantastic plant which has been awarded the RHS Award of Garden Merit, stand it in a bucket of cold water for a couple of hours then plant it about 6 inches deeper than it was in its pot, every February butcher it down to the floor, keep it well watered all the time, don't mess with mamby-pamby feeds, this is a toughie and will reward you with masses of Summer flowers.
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Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.