P11D Error - How to correct it?

Decap5

I find myself in a situation I've seen posted here before, but unable to find an example of the resolution:
A former employer sent in a P11D to HMRC which was in error, and I now have a tax liability. 
- I notified HMRC and the employer immediately when my P11D was issued. They acknowledged the question, but didn't confirm the cause of the error.
- The P11D is for the tax year after I left the company, so there should have been no residual costs left over. 
- Nevertheless, a corrected P11D hasn't been provided in time to affect HMRC's assessment. Needless to say, I don't have this extra cash sitting around... 

Has anyone had success getting a former employer to make corrections? If I pay HMRC to avoid further penalties, can I invoice the company for their error?

Decap5

I've just had a fruitful conversation with HMRC, so in case anyone else runs into this issue:
I watched the erroneous tax liability disappear from my Government Gateway account in real time, and got a new tax code issued to boot. (Total time ~2 hrs)

Steps:
- The Main HMRC helpline referred me to the Simple Assessment helpline (hold time: 1 hr)
- The Simple Assessment helpline put a Hold on Recovery Action and transferred me to the Income Tax Helpline (hold time: 20 min)
- The Income Tax Helpline compared my P11D to the P45, *which confirmed my leaving date*. The agent determined the last P11D was suspicious, was able to take action based on that. They also noticed a P11D was mistakenly applied to my current employer, and having confirmed no P11D was actually received, they corrected the resulting tax code error, which would have affected my liability in perpetuity. (Hold time: <5 minutes)


Lesson learned: When HMRC says "We can only act on the information we're provided," remember that the info they're provided isn't just the form in question, but the other forms, such as the new P60 and P11Ds from current employers, P45 from last employer, and the dates included in each. They were sympathetic to the fact that a former employer has no incentive to fix ex-employee records, and never mentioned the stated XX-day window to protest a charge.