I don't think the knife is the problem. As stated, the law allows for a fixed blade or lock knife with good reason.
I think a greater problem would be the tapping itself. Given the fact that its by a main road, you must ask yourself: What do you think a copper would do if he saw you banging your knife into a tree?
Remember that there is no public land in the UK, it's all owned by a person or group AFAIK.
I personally wouldn't bother. If you're going to do something of questionable legality, it's arguable that by a main road is the best place to do it
All will rise again for a better day; earth, green, with waterfalls where eagles hunt their prey