That happens, you can leave and they will go away or you can brush up/pick depending on size.

Hopefully like drc726 says they will go away, sometimes when you get alot of wet weather you get odd mushrooms growing up but take them up carefully and the lawn should be ok, however if you have the start of fairy rings then that can be a problem, they form a large expanding ring of mushrooms, and once they naturally die away you have a noticeable darker ring of grass for a time, fairy rings normally affect lawns mid to late summer and into autumn, but on occaisions due to weather conditions have noticed this take place earlier, very difficult to eradicate, hopefully you wont have fairy rings though.

The most likely source of the toadstools is the turf itself - seems to be a common thing these days. As Drc says, just twist them off - they're only the fruiting bodies of an underground root system, about which you can do very little.

You can pick them out of the lawn, but don't eat them, as many fungi look like mushrooms and can be deadly! Just get rid of them in your council compost bin. Annie