OK, so I never thought I'd say this, but I received superlative customer service.
Sorry it took me so long. I've been a little to-the-coast (I don't know entirely what this means. I heard it once in a Woody Allen film. I think - hope - it means busy).
So my Virgin Media operative arrived and rang the doorbell downstairs. Initially, I was worried because even though I buzzed him in, he didn't actually come in, and I had to run down and let him in. Seems as though he wasn't door-enabled.
He said, "I gather your cable modem doesn't work". And I said, "no, it works, it just does something odd to my wifi, and I now have two wifi routers. So you're apparently going to change the cable modem."
He said they don't support wifi routers. I was starting to feel all oh-dear-what-shall-I-do, as I know that I can't make inbound calls to the Virgin Media customer care operative, they only receive calls. But a smile and flash of cleavage (I made the last bit up, he was just fairly customer service focussed) and he plugged everything in, although it did take a few goes and we had to draw a diagram of our daisy chain. Also, he didn't understand why the wifi router was right next to the cable modem, because "it's wireless, innit." I persauded him the wireless router needed to be plugged into something to give wifi to all the other things.
Anyway. Seven-inch version: it works. It took ten minutes. And if I can find the receipt for one of my wireless routers and fax it to Mary at Virgin Media, they'll credit my account. Now, that's what I call customer service.