Why can’t BT connect me to broadband on the edge of London?

When I moved house the provider didn't process the switch, and now it says the local fibre cabinet is full

We have just moved into a house in Woodford Green on the edge of London but BT is unable to offer us broadband. The previous occupant had it, and as soon as I had a moving date I asked BT to switch us. However, it seems that this was not processed properly and the connection has been given to someone else in the road.

Incredibly, BT has told me that the local fibre cabinet is full, and there is no longer an old-style copper line connection. We need wifi to work at home and can't believe this is happening in 2022.