I do apologise, then you do need to find out why your tax code was BR. I feel (and I hope I am wrong) that you started this new employment and either the P45 was out of date or there was something on it that the employer could not use, and that a P46 was given to you to complete that was never returned, and they then followed HMRC instructions and used code BR ( I should advise these rules have now changed and code OT is used, which ensures that the right tax bands are used)
ONly HMRC can offer you advise why it was 2 years later from their originating correspondence, as to why they failed to chase up for this unpaid tax, and I suspect it was the PAYE unpaid position (which allows the issue of the P800) which cannot be carried onto the self assessment record, was overlooked, and its only now (due to the fact that the majority of the Southern tax offices, who are undertaking compliance and list work) this has been identified, but again this is no cause for appeal I am afraid to say.
As you wish advise without establishing facts first, all you can do, at this time is you get a letter of appeal in arguing employer error, as it was the employer that placed you on code BR at the start of your employment, but be mindful of the fact the position of the use of code BR might be due to your failure to complete appropriate forms for the payroll section of your employer.
And on the basis, start thinking about offering HMRC a payment plan to pay this tax off. If you are in anyway in a position to offer a half lump sum, then do so, as this will be looked upon more favourably by HMRC, in terms of accepting the other half paid by payment plan, but if you can make this payment term last no longer than 1 year, then HMRC are more likely to accept the offer.
But I can assure you there is nothing dodgy and if you see yourself you were on code BR for 2009/2010 you can easily see you have not paid enough tax, as all income would have been charged at 20% when some of it would have been due at 40% (although this would then be lesser than it would have been due to the fact you also were given personal allowances either)
I know its bad management on their part, and I agree there is no excuse for that, and I fully appreciate the impact this has on your life, but you could have drawn this matter to their attention, as you would have suspected that the BR issue did in fact relate to as far back as May 2009, and you have had the benefit of being paid too much with insufficient tax being deducted, and knew that had only pursued you for 2010/2011 onwards and it is (as far as HMRC are concerned) as much up to you in making sure your tax affairs are in order, ass its HMRCs.And unless you brought this to their attention, or had not been in the self assessment system then this first year of 2009/2010 would have been pursued long before now.
So its circumstantial there has been a delay, rather then sufficient in itself to argue grounds of appeal, and the only way to argue this, is employer error, if indeed its the employers fault, and you will need to ask HMRC to look into this, and /or approach the employer yourself to establish what took place with the tax position at the start of this employment.