Not an easy one. The obvious thornless choice is Zephirin Drouhin but she's one of the worst for downy mildew, and is often completely defoliated by the end of June. She prefers traffic fumes and clay! David Austin list 8 or 9 thornless climbers/ramblers. Have a look at theirs and give them a ring to ask. Many roses will flower very well in less sun than is thought they require, and the ramblers are tough plants. Bear in mind that most ramblers are not repeat flowering (a few are), climbers mostly are. Look at 'Amadis', 'Snow Goose' and 'Violette'

I have this one Phil.....not totally thornless, but very beautiful. some blackspot on the foliage....but I have terrible trouble with that here all the time....Mine grows well on a north facing fence.

Botanical name: Rosa 'Bleu Magenta'

Other names: Rose 'Bleu Magenta', Rambler rose, Thornless rose.

Variety or cultivar: 'Bleu Magenta' _ R. 'Bleu Magenta' is a Rambler rose. It is a vigorous shrub with shiny, bright-green foliage and few thorns. In summer it produces slightly scented, double, deep violet flowers that fade as they age.

Awards: RHS AGM (Award of Garden Merit)

Or try Peter Beales in Norfolk (www.classicroses.co.uk) they offer a couple of 'not very thorny' including Clarence House which is supposed to be vigorous. Quite a good plant selector (by colour, height, type, thorns ... And so on)

Fryer's (near Manchester) (http://www.grosvenorgardencentre.co.uk/fryer/) might have something but their website doesn't have much in the way of a plant selector beyond the main categories such as 'climber', 'floribunda' etc.

I have Zeph dro in east yorks and so far no problems.