If you know which companies the shares are held in, it's pretty simple. Contact the company and find out their registrar details.
On the basis that it's never going to be that simple, it may be worth contacting some of the larger UK registrars* (Computershare, Equitini, etc) to see if they can help. They will need to see a certified POA before supplying any information and it's possible that they are unable to search by name across all share registers, but it's worth a try.
*All UK limited companies must keep a record of who owns their shares. Many companies can't be arsed to do this themselves so outsource it to specialised registrars. It's been many years since I was in this line of work but I doubt much has changed.