Thanks for your question
There is not recourse against HMRC for failure to make the appropriate updates, as this also would have been your responsibility to ensure that your tax code reflected the correct benefits, and there is always a shortfall along the way, under normal circumstances, as your tax code for the present year, is always based on the previous years P11d, which appears to be the case here - that your 2009/10 code contained information relevant to 2008/2009 - and this is where the tax has fallen short.
Your employer is no longer obliged to inform HMRC of changes throughout the year, so this falls to you to ensure HMRC are aware of these, to ensure the correct tax is collected throughout the year.
Did you have a change during 2009/10 that increased the benefits provided, or maybe this matter actually relates further back. HMRC should have given you an explanation on the P800 how this unpaid tax has arisen - and you should be able to look at the 2009/10 tax codes you were issued and compare this with the 2010 P11d - and see for yourself whether insufficient benefits were included in your code.
I am afraid there are very little free specialist tax support services available, and those such as Tax Aid that exist are means tested (on low incomes) to help those not in a position to afford accountancy advise/representation, See link here for Tax Aid
So if you feel you have a good case to argue then you may need to engage an accountant, but do appeal initially yourself if you feel you have grounds to do so, but in my honest opinion, this is a new debt and the 2010 P11d would not have been sent into HMRC until after July 2010 and aside from the fact it has taken HMRC a while to get around to dealing with your P11d, you could have informed HMRC of any changes along the way to minimise this tax position, and that I am afraid is what they will argue against.