When the original infrastructure was installed, the construction teams dug up the pavement & installed a conduit leading from the street cabinet containing the connectors to outside each house local to that cabinet - no cables installed at this point. When they come to install your service they have to be able to connect a cable to the street cab & pull it through the conduit & thence to your property.
Unfortunately in your case the conduit is blocked, probably by over enthusiastic use of concrete during the initial construction, and will need to be cleared, before the cable can be pulled through.
- I'm surprised it will take a month, I had a similar problem that delayed my installation by about a week, but there were a lot more construction teams employed, back then.
All I can suggest is to keep calling to see if the installation can be brought forward, at all? - however, as you don't have to be there when the construction fault is cleared, it isn't as simple as hoping for someone else cancelling, and more likely due to overworked contractors???
<edit> to acknowledge Chris types a lot faster than I do
