I only mix the C-41 developer and stabilzer myself. All the chemicals are [or at least at the time] could be easily gotten from
I don't know if they ship to the UK but if they do the cost of the shipping would hurt.
I can't see any reason to mix anything but the developer and maybe the stabilizer. I know the bleach isn't cheap but it keeps fairly well. The fixer shouldn't be an issue for you to pickup. It also keeps fairly well. If you can find a supplier selling to mini-labs etc then see about buying big [5 litre or maybe 2litre no smaller] jugs of bleach and fix.
If you really want to mix your own bleach and fix then skip the blix. Use the alternative bleach and fix.
The demand for CD-4/CD-3 isn't set by the home market it's by people like Kodak,fuji etc mixing huge amounts of this stuff.