Hi atolhurst,
Just a wild guess ( if a photo is not possible) It sounds like it could be 'Woodrush' (Luzula campestris) It is sringy to walk on which may account for the rubbery texture that you discribe.
It can be common in lawns, especially damp ones that have also become acidic.
It's the flower that helps to distinguish it from true-grasses, I have put a link here that may help you to identify it, just click on 'woodrush' for the image-
http://www.lawnrestore.co.uk/more_informationh tml
Good Luck. Tbird+