From your description, the holes appear to be very indicative that they have been made by a badger. A badger’s home is called a ‘sett’ and many setts are made up of numerous entrance holes beneath which will be several chambers and tunnels. They’re usually shaped a little like a letter ‘D’ which has been placed on its side and tend to be anything between around 8 inches and a foot in diameter.
You mention that your dog has not messed with the holes so there wouldn’t be any problem for you to continue to walk it in the area. Generally speaking, badgers will avoid dogs as long as they’re not cornered by them as they’re not vicious creatures. However, if they felt under threat by a dog, they would be prepared to attack it as a form of defence and, particularly if your dog is small, injuries can result. Being bitten by a badger can also result in the spread of disease. That said, there is no real problem here so long as your dog shows no interest in the holes.
The other important thing to remember, however, is that badgers are a protected species under the Protection of Badgers Act 1992. There are numerous offences covered under this Act including disturbing a badger whilst occupying a sett as well as any damage to the sett – man made or caused by a dog. As you’ll probably be aware, badger baiting is an illegal activity, punishable by a fine of up to £5000 and it can even result in imprisonment. And, whilst all that you are doing is walking your dog, for the purposes of the offences contained within the legislation, it is assumed that a person whose dog interferes with a sett is guilty of trying to dig for, injure or even kill badgers unless it can be proven otherwise.
However, as long as your dog isn’t interfering with the sett, then you can rest assured that if there are any badgers in the area, they are not going to rush out and attack your dog. So, as long as you have permission to walk your dog on this land, there aren’t going to be any problems.