Andy (and Clive).
Clive has a good point here re. fuel tap, I did discount it first as you said there was fuel in both tanks. To relate an experience of a MW I used to look after for a customer, he ran one tank dry and switched over, from then on had trouble. Eventually after checking everything, I used a vacuum pump and guage on the fuel line, engine side of tap and found that although the tap was switched to the full tank, it was drawing air on the empty tank. As you know, they are a push-pull tap with a cork inside, someone had soldered it all together in the past and it was impossible to renew the cork, so I fitted a 2-way lever tap from an Austin on there with no further trouble. Another thing is that you now say the plugs appear to be wetting so getting fuel, is it possible a bit of crap from the tank you emptied, has got into the carb and blocked a jet in the idling part. You should have a guaze in the pump and another in the carb banjo, but they are often missing. A modern inline disposable filter is a good idea, better than keep stripping a carb.
Richard