Your employer will already be handling this, through the PAYE system.
Firstly, normally the allowance is applied automatically when tax is being deducted from your pay; it's shared out across the year so you get 1/12th of it each month.
In your circumstances, you should have filled in a form P46 when you started work there. That would mean that your employer will know that the allowance was unused from April 2011 to September 2011 and so it'll all be shared out for the remaining part of the tax year. Your payslip should show what's known as a "cumulative emergency tax code", which I think would be something like 1280L in your circumstances.
So in summary it's unlikely you will get any repayment at all, if the system has worked right. It is possible for things to go wrong though, particularly since your question title says you've been paying "full tax". If that does happen, then after the tax year ends on 5th April 2012 and you would then need to wait to receive a P60 from your employer showing your total taxable income and tax paid for the previous year, then contact HMRC for repayment. So you wouldn't get any refund on 1st April.
P60s normally appear in May or June after the tax year ends. You can use the HMRC tax checker to see if you'll be due a refund. But I'd advise you not to be counting on anything!
The other thing to be aware of is that you'll actually be paying less tax per month this tax year than you would next tax year, because of your personal allowance being spread out over fewer months. So you may also see your income drop a bit in April and you should be ready for that.