If you look on the back of the share dividend certificates you will probably find that a Share Transfer Form is printed for completion when you sell the shares. Unless you transfer the shares to your bank or stockbroker to hold under the CREST system on your behalf, you will need to retain the share certificates until the shares are eventually sold.
Your personal Capital Gains Tax allowance for the year ending 5th April 2016 is £11,100, therefore unless you sell a large number of small holdings you are unlikely to exceed your allowance.
The information regarding the prices you paid for your original holdings would only be known by you and your stockbroker. Likewise the value of share dividends are known only to you and the company's share registrars, therefore it is advisable to retain a record of the various prices you have paid.