It has to be said that climbers were bouldering at that particular spot long before anyone spotted the carvings. There's a series of graded routes, in the bouldering guide books, as far as I know. Whenever I've been to Copt Howe, however, it's mainly been the adjacent lump or uncarved sections of the main boulder that's been in use by climbers. In fact, the shot with a climber in shows a route down a side of the boulder with no carvings. Last time I was there I got chatting with a couple of climbers who were unaware of the rock art, but were fascinated by it once I pointed it out. To not notice it means they'd not even looked at it, which suggests the rock face itself was of no interest, and so didn't have a route for them.
http://www.themodernantiquarian.com/post/18056
http://www.themodernantiquarian.com/post/3401
http://www.themodernantiquarian.com/post/3402
If you look at Stubob's shot and my shots, they show (if you look closely) chalk marks down the 'corner' and side of the boulder. This means that's the bit that gets climbed, so I'm not sure that the carved face actually gets used so much - I've certainly never seen any chalk on it. Climbers don't tend to just go at a rock from all angles, it's a disciplined sport, and most boulderers will use specific graded routes. Having climbed a bit myself, and going from my (admittedly not the most trustworthy) memory, I can't actually see the carved side having a route on it... I may well be completely wrong. I've had a quick scout for route descriptions online but there doesn't seem to be a comprehensive online climbing guide, as most climbers use books.
Climbers aren't (in my experience) a bad lot on the whole. All of my climbing friends have a huge respect for nature and sites such as this, so I'm sure that if necessary precautions were taken (a sign explaining the significance of the spot) most would use other boulders. The Langdale valley aint exactly short of other climbing spots, after all. There's no accounting for random idiots though, and in that case, even a ban wouldn't be effective, unless someone was there keeping watch, which is obviously totally impractical.
Finally, how big a threat is climbing to that particular rock anyway? It's a very hard solid stone, from what I remember. The carvings look like they took real effort - they've been made by pecking, and are extremely faint - this is extremely tough rock! I can't see how fingers and soft rubber soles could do that much damage.
I really don't mean to say there isn't a problem, btw, just playing devil's advocate. If there's a genuine threat then something simply has to been done.
IronMan
PS - A good way to put climbers off using that face would be to say that the holds are man-made... a lot of them don't like that kind of thing :-)