Well, a quick update.
Other half (the one with the driving licence) totally unreasonably refused to do the estimated 15 tip runs needed to clear the 30-odd rubble sacks and other general detritus (old giant coldframe, metal poles, concrete posts...).
So I had a look at the Lewisham list of approved (!) rubble collectors and picked out a bloke called Santos as being nearest to us. He quoted £165 for 500kg of removal of rubble etc, which is what he estimated we had on a drive past. He took the lot, mentioned that it ended up being more like a tonne, but charged the same price and left it spotless. He even took stuff I hadn't expected him to, like some old waste bags full of pebbly topsoil and weeds that had become overgrown after sitting in the front garden for over a year (yes, I am a Bad Neighbour). And he was happy to wait for payment as I was off on a work thing for three days, on the middle of which he took the stuff.
We likee Santos a lot.