Don't panic.
As you have discovered there is no way that you can file online before the normal deadline for Self Assessment returns.
You should have notified HMRC of your additional income by 5 October 2012. Because you did not you are liable for a penalty calculated as a percentage of the Potential Lost Revenue which is the tax that should be paid by 31 January 2012. You can therefore avoid this penalty by paying any tax due within the next 2 days.
If you do this you will not be late paying any tax and so there will be no late payment penalty.
As you have not been asked by HMRC to submit a tax return you are not liable for the automatic £100 penalty which applies to those who have been asked to and do not do so on time.
I am going to assume your untaxed income is less than £2,500pa and your total income for 2011/12 is less than £42,475. Work out your income on the extra work (this includes all work done even if it has not been invoiced) up to 31 March 2012. Deduct any allowable expenses. Take 20% of the the result; this is the amount of tax you need to pay by Thursday.
In order to get there on time you need to pay by Faster Payments from a UK bank account (i.e. internet or telephone banking). Pay the money into this account. Those details say that you should give your Unique Taxpayer Reference (UTR) but it is unlikely that you have one of those (they only tell you what it is when you register for self assesement) so use your NI number instead.
Before you do that, ring the Newly Self Employed Help Line and explain everything, including that you intend to make a payment to Cumbernauld (they may give you a different account or your UTR to make life easier but if they say you don't need to make the payment I'd be inclined to ignore them - much better to have overpaid and need to claim it back than incur a penalty). Make sure they know that your earnings are below £2,500 a year; they may give you a different number to call (which will probably be a lot busier and staffed by less knowledgeable staff so try and get as much out of the Newly SE dept as you can). Write down details of this and any other conversation with HMRC and ask for the name of the person you are speaking to - usually best to say at the end of the conversation "thanks for your help, can I ask who I have been talking to?" rather than demanding their name, age and inside leg measurement at the start.
Finally, note that if you have PAYE income and your other income is less than £2,500pa then this is normally dealt with through your PAYE code, and they may deal with this on the phone however because this is late they may require you to register for Self Assessment. If they do you will have 3 months to submit the return: don't leave it to the last minute 
Hope that helps you and anyone else in your situation - note that if your untaxed income is over £2,500 you will have to register for Self Assessment, and if it is over £5,000 it gets more complicated.