Difficulty finding a place selling flat 3 core and earth / 4 core

I have never seen such a cable. If it exists I would think that it is special order and very expensive.

It is always best to buy from an electrical wholesaler. I would advise that people B&Q and Woodies type places for electrical cable and accessories. They are simply too expensive, have less choice and frequently products are of less quality than what can be found in a proper electrical wholesalers.