Hi, You don't say whereabouts you are or what type of soil you have. We are on heavy clay, which cracks open when there is a shortage of rain (like now!). We have grass over the deep cracks and if you pull the grass away you just find these great holes.
Could be you are on clay and it has shrunk with the drought, the grass stays where it is because the roots are matted together. Bad for your ankles when you suddenly drop down a hole.
If you don't have loads of grass you could try watering it, but I have never found this particularly works - the water disappears down the holes, probably for miles!
If it is clay shrinkage you will find cracks or drops in the other areas too, have you checked for that?

Is the grass still green, or have the roots gone as well?

Thanks for the info Honeysuckle, you're spot on in what you've said! There are cracks in other areas of the lawn too - I'll have to be more careful now when I cut the grass! Incidentally, I'm in East Yorkshire and am on clay! Thanks again for your reply.

Glad to be of help, even if the bearer of bad news! We have this problem which is part of the reason I am replacing most of the grass with shrub/flower beds, I shall just cover the holes with compost or bark and won't be plodding about over them. The small amount of grass I shall keep I am optimistically hoping to keep the holes filled with loose soil, but it will probably always look like a patchwork quilt. If you think the East Anglian Fens are all beautiful peaty soil - think again!