Question 1: Did you have any income which wasn't taxed at source during the tax year 2013-2014? (It doesn't matter how low it was. Even being paid for a couple of hour's baby-sitting for a friend can count - although, of course, HMRC is highly unlikely to find out about really trivial things like that!).
If your answer is 'Yes', then you need to answer Question 2:
Did you submit a paper tax return by 31 October 2014, or an online one by 31 January 2015?
If your answer is 'No' then then the explanation for the penalties which you're now facing seems obvious. If you have untaxed earnings (however low) you MUST
(a) register for self-assessment ; and
(b) submit a tax return each year.
If you fail to submit your return by the relevant date you automatically get hit with a £100 penalty on the following day. So, if you failed to submit an online return by 31 January 2015, you automatically had a £100 bill to pay on 1st February. (It's completely irrelevant as to whether you owed any tax or even if HMRC actually owed you money at that point. If you didn't send a tax return in, you have to pay the penalty).
After three months (i.e. from 1st May) additional charges of £10 per day are applied for the next 90 days. (So you'd then owe a total of £1000).
Additional penalties are levied further down the line, so it's not hard to see where your big bill has come from.
More information here (together with some possible courses of action):
http://taxaid.org.uk/guides/taxpayers/tax-returns/late-filing-penalties-and-appeals