Yes, that is a viable option. Loads of people who do the walk camp all the way, varying from campsites to wild camping (which is legal in Scotland, and generally accepted in England if you respect where you're camping).
I haven't done it myself - I'm way too soft and pampered! - but if you take a look at the links on my Useful Links page:
and take a look through some of the other walkers' journals listed there, you'll come across a lot of campers. It's the most popular way to do it, given the cost of accommodation and the length of the walk.
I hope this helps, and good luck with the planning!