After much research and some experimentation, I worked out that the likely cause of my starter's feeble constitution was that I wasn't keeping it as warm and cozy as it would prefer. According a Sourdough Starter article on Wikibooks, the optimum temperature for the growth of Lactobacillus sanfransicensis (one of the two main yeasts which are responsible for the rising properties of a sourdough) is about 32°C. Well, I certainly wasn't keeping my starter that warm!
So, at the beginning of the week, I tried putting George (my sourdough starter) on the windowsill in my utility room (which is basically a glassed-in side-return of the house and which is south-facing so it gets very warm in there) on sunny days or in a coolbox with a nice snuggly warm hot water bottle next to him on cooler days. Sure enough after a few days of this luxury treatment, we reached the magical day (yesterday) when George doubled in size as a result of being fed (well, I think he did. I worked at the office rather than at home yesterday, so am only guessing by the marks on the side of the glass jug, but my other half pointed out that those marks might well have been where I scraped the mixture down the side of the jug).
Anyway, last night I made a sponge according to Hugh Fearnley-Whittingstall's recipe on the Guardian website. This morning, the sponge was indeed springy and bubbly, so I joyfully made a start on the dough - giving it a good, solid knead - then I left it in the kitchen to rise. At lunchtime, it still hadn't risen much, so I moved the dough to that nice warm utility room I mentioned. At about 4pm today, when I went to make a cup of tea, I took a peek and decided it had probably doubled. I turned the oven to its lowest setting and let it warm up (to about 50 degrees) while I knocked the dough back, shaped it and placed it into an Ikea food saver lined with a flour-dusted tea towel. I covered the dough in an oiled plastic bag and put it in the oven (on a cork mat so I don't melt the plastic tub and with the oven now turned off). By my estimation, the loaf should have doubled and be ready to bake by about half past six, just in time to have fresh sourdough with dinner. Fingers crossed!