I think this is probably Mycena flavoalba which is very common on lawns, can have a yellow or whitish stipe and shows the striations you can see on the cap. As can be seen by the short grass blades this is a very small and delicate fungus and is easily damaged.

In the grass in our garden, Cheshire 30th September 2004

Added on 1st October 2004, amended on January 29th 2005, updated 19th Nov 2014