They did attempt to do that using spot checks during the lockdowns (I think they are currently), so they could resort to this if need be.
I have another interesting theory; Boris said that “all legally binding restrictions on social contact” will be removed on 21st June if all goes well. Do you think this would allow Alton and the UK’s other theme parks to operate without social distancing, masks, pre-bookings etc after this date, or do you think he was purely referring to household/private mixing? He did say that things like nightclubs would be allowed to open, people would be allowed back into sports stadiums, and limits on things like weddings and funerals would be removed, so I think it could possibly mean the former, although I wouldn’t want to be too sure.