As far as I am aware there are 3 breeds of Swan in the UK, the most common being the Mute Swan, there are also the Whooper Swan and Bewicks Swan. They all have a brood of between 5 and 8 eggs.
Male Mute swan
The way to tell Male and Female Mute swans apart is by the knob on top of the beak, in the Male it is significantly larger.
Male and Female Mute Swans (Male on Right)
Female Mute swan with young Cygnets
I love this picture as it gives an idea of the size of the swans wings.
People have asked me many times how I get my close ups, so here's a short video which should answer the question...