Skylon was designed by the same people who designed HOTOL. It is their way of getting around all the problems they encountered on the first attempt.
It's large because it is powered entirely by liquid hydrogen (relatively low density) and liquid oxygen and because nothing falls off it at any point - unlike multi-stage rockets. The design life is 200 flights per vehicle which is what gets the cost per flight down.
The design they show people is the C1 configuration with a 12 tonne payload to an equatorial orbit. They don't show off their D1 configuration which I believe carries 15 tonnes with better performance.
The heat exchangers in the engines are the primary enabling technology and a lot of effort has been put into proving them for that reason.
A way to sum it up is that the heat exchangers allow them to not have to carry 250 tonnes of liquid oxygen onboard which they get from the air as they ascend instead.