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Update and responses:
Late last night, I decided to give the one I'd just chucked in the bin one more try (it was quite an expensive one by comparison to all the others that I'd binned, so finances dictated a reprieve, if at all possible). Pressed the button and, hey presto! a flame!! And yet, I'd tried it again and again and again over about half an hour before, and nothing. So the thing's back on the worktop for the time being.
To the various respondents:
Matches, even the extra long ones, are never a good idea, when you're reaching to the limit of your stretch, into a dark corner at the back of the oven. The cooker has a fairly narrow space in front of it, which limits how far down on my knees I can get. A long-nozzled gas wand sorts that problem out.
SandyRoe, the suggestion of the battery-operated lighters is, on first sight, a good one - but a lot of reviews of the various types sold on Amazon are rather negative about the spark's unreliability to actually light the gas. And if I went for one which operated a spark to light gas from it's own reservoir, then we're going round in circles, and back to the same problem.
And yes, Heathfield, I do know how to fill gas lighters from the canisters sold in newsagents, etc. I used to smoke for many years (thankfully managed to kick the dreadful habit in 2007), and regularly refilled my transparent lighters with those canisters, so I could always see the level of the gas rising. I think a lot of the trouble with gas wands is that the gas reservoir is buried quite deep within the body of the wand, and the valve is barely accessible through the tiny aperture at the bottom end. So you're never quite sure if the end of the nozzle or adapter is making proper contact with the valve. Without taking the thing apart, it's pretty much down to trial and error. And although there is usually a long, narrow plastic window through which you can ostensibly view the level of gas, in reality it's almost impossible to see it. I'll bear in mind your suggestion of the Cricket lighter, as the brand is quite well-known, and has been around for decades.