It is classed as a trailer so if it has brakes they must work, in reality you are highly unlikely to be stopped and checked in the UK, I have never been stopped in over 30 years, first 8 or 9 years I towed a 1988 Fiat Panda which weighed 700kgs, home made A frame without brakes and never had a problem, I understand if you don't want to drill holes in a classic car for a cable linking to the brake pedal but there is a way around that, not cheap though unless you can buy a second hand one
It is a brake buddy, an electronic braking system which costs around £1500 new but they do pop up regularly for £500 or so, I bought one from someone on another forum complete with A frame for £50, I saw the ad when it had been posted for only 15 minutes and thought it was a misprint, I messaged the seller and he said it wasn't a misprint but he had already had his money's worth from it, I had to drive to Great Yarmouth to collect it but it is great, it sits in the drivers foot well and connects to the brake pedal, it has a built in compressor so when you brake it automatically brakes, even a broken one would be OK for you, at least it would appear legal
As far as towing your car you are limited to trailor speeds, 60mph on motorways and dual carriageways, 50 mph on single track roads, stay out of the outside lane on motorways etc
I have my old A frame (braked) which could do with a fresh coat of paint but I I am sure you could do something with it, you can replace the over run hitch with a standard trailer hitch so if you want it then it is yours, we should be able to get it up to you, I will post a picture tomorrow