But the working assumption would be that those issues are likely to be worse with tin, zinc, etc, compared with lead?
Not to mention the challenge in a - hopefully long? - transition period in the U.K. in which unlicensed guns must stay below the 12/6 limit with the most efficient lead ammunition, and would therefore be carrying less energy (or shedding it more quickly over distance) with non-lead, affecting effective hunting ranges.
And, setting accuracy aside, this would be with a less deformable projectile. Personally, I think projectile deformation at, at least, subsonic velocities without complex design (eg Hydra-Shocks and other clever pistol-range JHPs) is often over-estimated as a factor across small arms, and is largely irrelevant to head shots on typical airgun quarry, because they are head shots, but others differ.
So, sub-12, and at “normal” distances, you appear to be looking at less precision, lower impact energy, and lower potential wound ballistics. And use of a larger calibre, reducing effective range, both by loopier trajectory and reduced precision.
A sensible approach would be to consider the impacts on public health, safety, animal welfare etc of less effective airguns versus more poison, trapping, shotguns, rimfire and so on.