Strange Holes in my Lawn

Hi all i'm new to this but am in need of help if anyone has any ideas.
Could you help with holes in my lawn please. I have discovered 2 holes in my lawn about 2 inches across by 3 inches deep. There is no soil left around it, just the hole. I asked my 2 immediate neighbours if they have any and they came back and 1 said he had found 5-6 in his garden and the other about 5 holes the same. I have only just relaid my lawn so am really upset about it and am desperate for some ideas...can you help?? .. Thanks Kelly

 

Do you have badgers? A few years ago that was the sort of scrape that badgers made on my lawn when they were digging for earthworms.

 

I've got a couple of holes about the same size neighbour told me they belonged to bank vole's which are a bit like a mouse I think. Not sure if they are where they live or used to store excess food there was a tea bag just below the entrance of the hole the other day. I have filled them up several times only to find the hole back the next day.

 

It sounds like they have been dug by squirrels. We get them from time to time.
They tend to dig the hole and drop in a peanut. Unfortunately they aren't very good at covering them up, so the pigeons come along and take the peanut, so you rarely see a hole with a nut in it.

 

black birds and rooks do that, you could rig up your garden with 240v mains... then your find what ever is doing this will be fried