Yes, Ronski, that was my conclusion too. Most of the time the router/step-down/ups ticked along at around 9 watts measured at the mains socket, but I did see briefish increases to 13/15W when watching iPlayer, so I've speculated that at times, the board did an overload cut-off. Since moving away from that board, the Billion has not misbehaved.
I have ordered a 50W step-down board (rated at 38V max input), but this time I'll be using it with a high-quality 15 or 19V laptop adapter to get it down to 12V.......expected arrival 3 weeks. Obtaining a 52V>12V step down of 15W+ rating is a bit pricey for experimentation purposes, but I will keep a weather eye on possibilities, because I would like to return to the mini-UPS in the future, if possible.
[later update: I've now spotted a higher-rated board of 75W at acceptable price and will give that a try]
In the meantime, I'm powering my Billion with a largish (laptop-style) 230V>12V 5A regulated power supply that I have used to power one of my 12V mini-ITX computers very happily over several days via my normal UPS without issue. When I swapped the Billion away from its wall-wart 12V 2A adapter I immediately noticed a 'cleaner', minispike-free SNRM trace and somewhat lower error rates on up/down stream. I guess the psu is of higher quality than the wall-wart type.