A better use for grey water is to store in a reservoir for flushing your toilets. You obviously need separate plumbing for collecting the grey water and for the

A better use for grey water is to store in a reservoir for flushing your toilets. You obviously need separate plumbing for collecting the grey water and for the toilets. There are also recirculation pipes for lung runs of hot water piping, like hot water columns found in hotels. The return circuit doesn't need to be thick, two sizes downwards will do (for instance a DN15 pipe for a DN25 column). Both the column and the return need to be properly insulated. DHW circulation pumps are usually made of brass and come equipped with a no return valve. This layout does exactly what you describe but instead of going into the cold water pipe, it goes back into the boiler.