To much agreeing going here - but I agree too. Borough Market is great for what it is, an open Market with all the fun that brings, lots of different things, some unusual, some bizarre but it all adds to the colour. However, not the place to do all the mundane shopping. And, best of British? Well, some of it certainly is, some of is about the same as you can get elsewhere, and lots of it, and I suggest increasingly, isn't British at all. That's great too but we mustn't get overtaken by the heady experience of an open market flogging some fresh produce.
I don't understand the problem of having a supermarket near Borough Market, it shouldn't be a challenge. The open market will still be the place to get funny mushrooms, decidedly delicious but strangely flavoured cakes and odd shaped fish et al. and the supermarket will be the place to get loo cleaner and kitchen rolls. Works for me.