Having had some experience of cycling along a cycle path on my Brompton, I'd not recommend it.
It's not too bad when it's paved, but a year or so back I rode along Regent's Canal out towards Hayes. The first part was bumpy, but paved, so manageable. But once the concrete ran out, the Brompton struggled.
I don't have a specific recommendation, but if it's a canal you're thinking of, then I'd recommend looking something with bigger wheels.