Yes, I went for a folder in the end and got the Mezzo I4 I was admiring. I rode it home, and managed not to get squashed or lost, although I will need to familiarise myself with the best routes, not to mention the bits to avoid at all costs (i.e. Bank).
Even over four and a bit miles, and with me not having ridden a bike for a year or so, it was comfortable and easy to ride. The only thing I do notice is that riding very slowly, for instance to creep between parked vehicles and stationary traffic, the small wheels make it a bit wobblier than I am used to, although they also make it rather more nimble.
The City itself wasn't too bad, although it's clear that I will do best by getting south towards Fleet Street / Cannon Street as soon as possible. Once past Tower Bridge it's onto the Cable Street cycle route, which is a joy to behold - a dedicated two-lane bike path, actually grade-separated from the (relatively quiet) road for much of its length.
I reckon on allowing 40 minutes for the journey, which should come down a bit as my cycle fitness and familiarity with the route improve. There are also some other ways in and out I could explore; the TFL cycle planner offers the option of going up to Mile End and in along Mile End Road, which I can see working - although I doubt it will be as quiet as Cable Street. And whilst I wasn't too uncomfortable, I can see myself following
purplecthulhu's advice to pick up some padded cycling shorts soon.