As you've suggested, Grandparents Day is an idea imported (by the card manufacturers) from the US. While some American ideas seem impossible to resist/supress - e.g. we seem to be stuck with 'trick-or-treat' - we've been doing remarkably well when it comes to ignoring Grandparents Day! The first time I saw cards for this was when I lived in Sheffield. Since I left Sheffield 15 years ago this means that these cards have been around for at least 15 years. The fact that you've only just noticed them shows how sensible the British public have been in ignoring them!
My advice: Don't buy the over-priced cards from shops like Clintons. If you've got little kids, don't mention 'GP Day' but just help them create their own hand-made cards which simply say something like 'I love you Grandma'. (What grandparent wouldn't be really pleased to receive something like that?). If you're at that stage of life where the grandchildren are adults (yourself, perhaps?) then phone up the grandparents near the date for a chat and tell them how much you'd like to see them - perhaps fix a date for lunch? This will be far more meaningful than any card.
Chris