As far as I'm aware there are no fungicides available in the UK that are effective against fungi. However, since they are not damaging to the turf, and are part of a natural and temporary process and even beneficial for your lawn there is no need to treat them. In fact it's a sign of a healthy lawn.

Break the stems by brushing the toadstools will cause them to dry out and disappear, they are composed mainly of water.

They are not damaging to the turf and are a temporary problem.

No treatment available, as Myron says. Twist them off at the base and pop in a plastic bag to dispose of them in case they're the kind which spread by spores from the gills if you like. These are just the fruiting bodies of mycelium present in the turf of which you are unaware most of the year - they will pass after a week or 3.

I just leave mine alone as they are gone in a few days.

You could kick them over before you ignore them if they bother you.

Often, increasing the population and diversity of your soil organisms will reduce the problem. I would apply a good compost to the lawn twice a year--or a good "48 hour" compost tea several times a year, for faster action.