Once your own child reaches the age of 16, they have the right to walk out of the door and make a complete break away from you. You have no right to know where they're living, who they're living with or whether they've got children of their own. So, following on from that, you certainly have no right to even know about the existence of your grandchildren, yet alone have any rights with regard to them.
However, as indicated in Happyred's link, some grandparents are fighting to change the situation. There's an example of this in this post:
http://www.theanswerbank.co.uk/Law/Question352 688.html
(I suggest checking out the link to the Grandparents' Association).
Chris