That's condensulate, at least that's what it was called. British Gas were installing it on virtually all their boilers at one stage (could still be I left a few years ago now) and they re installing Potterton Precision as their budget option.
It's the black corrugated pipe you see at the boiler end wrapped in white insulation and then a thin polythene cover over that. You run the condense in inch and a half waste and then push the condensulate down the inside of it. Stops the condense freezing.
You won't be able to connect your washing machine to it as it fills up the inch a half pipe.