Until independent scientific research proved them all wrong, many people claimed bikes caused far more environmental damage to trails than walking boots. However, research and testing is all very well, but you don't actually need to do any if you know where to look in the first place.
Take as an example Rushup Edge, Derbyshire. This runs west from Mam Tor, high above the Vale of Edale. There is a path - or rather, two paths - along the crest. From the western end, this is a single path designated as a bridleway. About halfway along, the path becomes a footpath and from here to Mam Tor it has a generous allocation of stiles. Where it becomes a footpath, there is a gate through the adjacent wall and a bridleway runs from this gate to Mam Tor, paralleling the footpath and wall for the entire remaining distance. This creates a wonderful opportunity to compare damage, as most riders pass through the gate and take the bridleway, whereas most walkers take the footpath - possibly to avoid cyclists, but more usually because it provides better views and a better surface.
Where the bridleway is the only path, the surface is very firm and generally dry underfoot, in many places worn down to the rock. This makes for good walking and great cycling, providing a solid surface that doesn't cut up in the wet and plenty of sections to keep you interested without being a huge technical challenge.
On the footpath section, the surface is virtually identical - firm, dry and worn to the rock in places. The parallel bridleway, however, is very different despite being only a few feet away. Basically, you're riding up a grass field the entire distance - it's a very boring, energy sapping slog with no reward. When it's wet, it gets boggy in parts and is even harder work.
Many people will by now be thinking "Well, that proves my point - the bikes cut up the surface and make the bridleway boggy". However, to think so is extremely blinkered and short-sighted. Why is the footpath and remainder of the bridleway so firm under foot? Well, it's because the multitude of users have, over several years, eroded much of the water-retaining topsoil from the path, hence the reason the rocks beneath are exposed in many places. The bridleway parallel to the footpath gets boggy purely because most of the topsoil is still there.
To look at it another way, the lone bridleway section and the footpath section are, as previously stated, virtually identical in terms of the condition of the path. Surely if bikes caused more damage than feet, it would be reasonable to expect that the lone bridleway section, which carries a heavy traffic of cyclists, would be in a far worse condition than the footpath section which doesn't. This is not the case.
Q., I believe, E. D.