Mushrooms and toadstools rarely do any harm to a lawn, but if you wish to remove them the easiest way is to pick them by hand (wearing gloves in case it is a poisonous species). You may also wish to use a brush, or mow them (with a box on the lawnmower to collect the pieces).
Two things can be done to help reduce the growth of fungi in the future:
Aeration results in increased root growth. New and stronger roots lead to healthier and stronger plants. September/October is a good time to aerate, at present we are recommending aeration as we visit all our customers who we know their lawns will benefit.