Blown exhaust?

Hi there, I was wondering if anyone is able to help identify my problem?

I have a 2003 1.2 ltr (petrol) Vauxhall Corsa, and as I was driving it home this evening down the motorway, accelerating from 60-70mph in 5th gear, I heard a loud pop coming from the rear left of the car.

Further driving, the car sounded a lot louder and raspier, but also kind of muffled.

Upon getting home, I've taken a look and it looks as if something has happened to the exhaust and there's a lot of hairy/fluffy stuff hanging out the pipe (picture for reference, sorry for the low quality: http://imgur.com/dHxayDV).

Can anyone suggest what has happened and - more importantly - what this is likely to cost me?

I've only had this car a month and a bit and it's been nothing but trouble. I've already spent £400 just getting a new BCM fitted (amongst other things) after the indicators all decided to fail on me literally the day after I bought it... all working at the point of sale. Sadly I got it off a private seller, so I have no way of demanding compensation.

Cheers for any help!