I usually replace worn out tubes with whatever 26" tube diameter I have to hand but should I be using a certain size for 26 x 2.1 tyres? I seem to get a lot of punctures and wondered if tube size had an impact.

Tubes usually have the size range on them,
eg 26 x 1.8-2.2. Just make sure that the latter range includes 2.1, as in this example.

But then I've been using regular tubes in my 2.4" tyres without a problem...

If your tyres are old they'll provide less protection.

I'm using a batch of WTB 1.95 - 2.1 that I bought in order to standarise all the Schrader/Presta combinations I had - I've got them in everything from 1.5 slicks to 2.4 fatties & it's been months since I last punctured so I don't think you are suffering from a mis-matched tube.

Lots of punctures might mean a rim tapem problem, I've used undersize tubes before and it doesn't seem to cause any problems.