Very old shares do not have book price

I have some shares which are the result of multiple years of employee share purchase a long time ago. There are therefore many different acquisition dates, and since their purchase a number of corporate actions and mergers of the parent company. In addition the company moved the custodian/holding bank two or three times. The net result is I have dates of the shares becoming mine but I don’t have the book costs and the company is unable to help. Can I take the average price of the dates of each record in the current bank where they are held and estimate?

Hi,
Yes as this would be seen as a S104 holding.
Shares and Capital Gains Tax (Self Assessment helpsheet HS284)
Thank you.