I tried this before, and the HDMI-VGA cable, being unpowered, was taking too much from the Pi, so it didn't work, it kept crashing.
I woke up this morning with an idea. Suppose I gave the Pi six volts instead of the nominal five? Maybe it would have enough to power the converter cable.
And it did. I'm writing this blog entry on a Raspberry Pi, with an awful keyboard, but running xWindows, using the HDMI-VGA converter, which now seems to be totally stable. My multimeter reports that the Pi is getting 5.7 volts. This means that with a £10 cable, you can run a Pi on a VGA monitor.
I called RS today to find out what's happening to the two Pies they owe me as replacements for faulty Pies. The lady there reminded me that this is a short-staffed day, but went on to tell me that it's been dispatched. Delighted, I asked when was it sent? "January 12", she said; this is obviously the RS-imperfect tense where "has been dispatched" translates to "will be dispatched if we get some on the date suggested". I didn't even ask about the additional six I ordered. One of them will be going to Ann, who is proudly clueless about computers, isn't really aware that I changed her from Windows 98 to Linux, and won't know, unless I tell her, that she'll be swapping to a Pi.
The good news from RS, though, is that the lady told me that they wouldn't be wanting the faulty Pi back; I guess it would cost them more to process the return than the £20 value of it. So if they stick to that, I'll have a go at repairing it myself; I'm not a perfect solderer, but I can bodge things together sometimes.