UK share transfer at Companies House

I own two limited companies in the UK. I'm looking for a UK-based freelancer, with a background in accounting and/or legal services, to assist with an intercompany share transfer.

The intention is to position the holding company as the shareholder/parent company of a subsidiary trading company.

I would like to avoid any capital gains tax and stamp duty during the transfer (my understanding is we need to use a J30 form, CS01 confirmation statement and Section 77 relief).