Toadstools in my tunnel

This has been my first full year with my tunnel, and one thing that's puzzled me a lot is the plague of toadstools that keep springing up in the beds. I've been ultra careful not to water the beds much at all, to the extent that some root crops have suffered from lack of watering. Even when the surface of the beds is powder dry, the toadstools still spring up. All vents and door have been wide open all through the spring/summer, day and night. I'm just starting to close the door overnight, but still leaving the vents open all the time.

Is it likely they could have come in with the topsoil? I've got 4 raised beds in my tunnel. They are sitting on top of soil, but I filled them with imported topsoil. I don't know what to do to get rid of them. I'm a bit reluctant to start chucking chemicals on the beds. I keep chopping them down but they spring back up again overnight, and there's an awful lot of them.