Just asked DP, who is a payroll manager.
He agrees with posters upthread: fess up to HMRC, and try and agree a repayment schedule. Presumably there will be others in the company with the same problem, so hopefully they will be sympathetic. Once he's agreed a schedule, he could ask for it be recovered through his tax code (ie, his tax code will drop and he'll pay more tax than he otherwise would for a while).
However, he also pointed out that it has been common knowledge for years that most company vehicles are a taxable benefit so he should have had some idea that something was amiss if he had the standard personal allowance.
A few years ago, before I worked for them, my employer increased our mileage rate to above the HMRC approved level. Somehow, no-one in finance realised and it was only when I asked when I'd get my P11D that they twigged.
They immediately did P11D's for everyone AND reduced the mileage allowance to the HMRC threshold. Staff who'd been there years were really pissed off about it, but thankfully no-one every knew it was me that brought it to their attention.
Responsibility for paying the right tax is a bit of a grey area imo. Once, when DP started a new job, he realised that his predecessor had somehow been giving staff two lots of tax relief on pension contributions and they had been massively underpaying (lots of people on 6-figure salaries). It ended up costing the company over £100,000 and they couldn't recover it from the staff as it was the duty of the employer to collect the right tax.