Thanks for the replies, chaps.
Done some more investigation and it would appear that you are indeed right - the acceleration side of things isn't delievering any fuel. The pumps seem to be working correctly, however.
Just had the carbs off the cars and in bits - cleaned out all of the jets and plunger bearings as far and as well as I can, they were very full of crud indeed. Hopefully that will have sorted my problems.
Out of interest, is there anywhere that will supply single parts for carbs, such as, say, a new diaphragm or a new main jet?
Many thanks for the input
Richard