I agree that English traditional singers typically sang in a free rhythmic style, but that descibes how they sang when they sang solo and unaccompanied. When they sang choruses with other people they would naturally have had to adopt a a more regualar rhythm if only for the chorus part.

Indeed, I suspect that it is being free of other people (i.e. singing solo) - rather than being free of instruments, that facilitates a freer rhythmic style.

If you're a lone singer accompanying yourself on say a fiddle or a squeeze-box you can vary the accompaniment to fit your irregular signing. The instrument wouldn't prevent this unless somebody else is playing it.

People made their own fiddles and there seems to have been quite a lot of cheap Anglos about in the later Nineteenth Century, so did ordinary people actually sing with them or were they used just for dance music? Do we have any historical references?