Legally? No, you can't.
Anything dangling along behind a towbar is a trailer. Any trailer with a max laden weight over 750kg has to have all wheels automatically braked by the towing vehicle. The dolly wheels might be braked, but the towed car's wheels aren't. Yes, you can get braked dollies, where there's a link to the towed vehicle's brakes - that's how all those Smarts behind motorhomes do it. The dollies are heading towards the price of a trailer, though, and I think you need a fitting kit for the towed car.
The only exception to that is "emergency recovery" - which is how the AA/RAC etc use dollies. There's limits to distance, and serious limits to speed.
Tow it facing the right way, the steering castor action self-centres it. Tow it facing backwards, and you're likely to find the castor action trying hard to chuck it to full lock.
B'sides, what happens if you bend or break something at the event? Can't tow it home. Or just get the swivels and FWHs full of water? You're still spinning stuff and wearing it rapidly (with knobs on, if you tow it right way round). The only sensible solution's a trailer.
