It is not unlawful to tow with a Twizy in the UK. That Twizy does not have EU type approval for towing means only that Renault never submitted it for consideration for approval, and as a consequence no one will manufacture any towing equipment specifically for the car.
If you can build - or have built - towing equipment that complies with the necessary EU regs then you could quite lawfully tow with Twizy. However, with the weight of a trailer and contents you would need to keep an eye on weights so as not to exceed limits for the vehicles class.
But lawfully and physically it's perfectly feasible, although potentially challenging.