A few of the shows I attend are now asking for proof of Public Liability Insurance.

Used to be the case of clubs/stalls/traders only needing it, but now they are looking for individuals to have as well.
Must be in case you close the door on someones finger or the bonnet closes on someones head and they try to sue

But does your normal road insurance cover this, or is it something extra that needs to be bought ?

I've noticed this as well and for the last almost 20 years have been an active helper at our local vintage show ( I show my car here as well) The main organiser has this in his entry form small print and I believe it was due to the fact that various stean engines/traction and stationery engines needed a loyds certificate for their boilers. This then went on to include many other " possibly dangerous" items such as the farm machinery etc.
I've always taken the path that my road insured car with third party cover would be enough BUT don't take my word for it.