At a guess, Sainsbury's website relies upon tracking technology to function fully. Firefox automatically blocks web-tracking by default, so it might prevent the ordering process from working. (Similarly, some websites report that Firefox users have got an Adblocker installed [even when they haven't] and won't allow access to them. The Radio Times website is among them).
I can't be sure that my theory is actually the cause of the problem but the Sainsbury's site definitely uses web-tracking, so it's certainly a possibility.
The next time you order from Sainsbury's, try Firefox again but click on the little shield to the left of the address bar. Then click on 'Disable protection for this session'. I suspect that will solve your problem.