Had you stayed in the same job for the whole tax year, I would have expected a full year's medical benefit to be £701 (£584 / 10 x 12) and your tax code to be £873L (£9440 - £701).
The fact that you changed jobs and no longer had the medical benefit for the last two months of the 2013/14 tax year would not have meant that your tax code for those final two months should have been 944L. Your final personal allowance would have been £9440 - 10/12ths of the annual medical benefit which based on the figures you have given me would have left you with net allowances of £8856 (£9440- £584), code 885L. That code may have been operated on a Month 1 basis in March 2014 which means that it would have ignored what happened in the previous 11 months and for the position to be squared up after the end of the tax year which is what appears to have been done.
The error if there was one must have occurred earlier in the tax year. There are two ways you can deal with this:
1 Give me the gross pay and tax for each month of the 2013/14 tax year so that I can work out what the monthly tax deduction should have been or
2 Call the tax office on the number here
(there are few local tax offices now) and ask them to tell you what tax codes were issued for 2013/14 by them and what was in them in terms of allowances and deductions, ie benefits. Ask them to confirm the medical benefit of £584 was as shown in the P11D sent to them by your former employer. Let me know what they say if you are still not convinced that the underpayment is correct.
The best time to get though to the tax office is early morning or just before they close. The only alternative is to write but you will wait for a long time for a reply.
I hope this helps but let me know if you have any further questions.