Where do you get information on companies offering reinvestment plans when Registrars like Computershare and IRG don't produce lists?

Go to www.google.co.uk

Imput "dividend reinevestment" in the search box.

Loads of links, including some for companies that offer them.
Sorry no time to search the whole lot, but hopefully you will find a list of UK companies there.

I hold a few Avis, and use this plan, and receive the odd shares in lieu of a dividend.