A quick Google of the UK paintball laws states that paintballs are legal because they fire a "frangible" ammunition which is designed not to penetrate the skin.
Regarding BB guns. Unlicensed BB guns are allowed as long as they are under a certain energy level. This link covers it fairly well.
http://www.airpistol.co.uk/airgun_law.htm
What will need to be determined is if a cannon will be classified as a rifle or a pistol. They each have a different maximum velocities for unlicensed use in the UK.
For .177 ammunition the limits are:
Rifle: 826 ft/sec
Pistol: 584 ft/sec
I think if someone in the US with a chrono can measure the velocities they are seeing from their guns, it would help too determine the possibility of the Hobby in the UK.
Steve