The tax due on your first trading profits for 2010/11 must be paid on or before 31 January 2012. In addition, if the tax to be paid for 2010/11 exceeds £1,000 you may also need to make payments on account for 2011/12.
Payments on account are due where the underpayment at 5 April exceeds £1,000 and less than 80% of the total tax due for the year was deducted at source, eg through the PAYE system. If you do need to make payments on account for 2011/12, each one will be 50% of the previous year's liability, becoming due on 31 January and 31 July 2012.
If the tax due for 2010/11 is less than £2,000 and you submit your 2011 tax return to HM Revenue & Customs before 31 December this year, you could opt to have the underpayment collected through your PAYE code from 6 April 2012. This method of payment is beneficial from a cashflow point of view, but also means that you do not need to make payments on account for the 2011/12 year either.
There is one more consideration that you need to make and that is regarding National Insurance. As a self-employed individual you need to be registered for Class II National Insurance, but in addition your profits may be subject to Class IV National Insurance. Where an individual has both employment and self-employment income, consideration needs to be given to claiming deferment for Class IV National Insurance, in order to avoid a potential overpayment. The rules governing the interaction of Classes I, II and IV National Insurance and complex and you should therefore consider seeking professional guidance.