Just to clarify the statutory position here, regulation 72 of the Income Tax (Pay As You Earn) Regulations 1996 states:
72 Recovery from employee of tax not deducted by employer(1) This regulation applies if—
(a) it appears to the Inland Revenue that the deductible amount exceeds the amount actually deducted, and
(b) condition A or B is met.
(2) In this regulation and regulations 72A and 72B—
“the deductible amount” is the amount which an employer was liable to deduct from relevant payments made to an employee in a tax period;
“the amount actually deducted” is the amount actually deducted by the employer from relevant payments made to that employee during that tax period;
“the excess” means the amount by which the deductible amount exceeds the amount actually deducted.
(3) Condition A is that the employer satisfies the Inland Revenue—
(a) that the employer took reasonable care to comply with these Regulations, and
(b) that the failure to deduct the excess was due to an error made in good faith.
(4) Condition B is that the Inland Revenue are of the opinion that the employee has received relevant payments knowing that the employer wilfully failed to deduct the amount of tax which should have been deducted from those payments.
(5) The Inland Revenue may direct that the employer is not liable to pay the excess to the Inland Revenue.
(5A) Any direction under paragraph (5) must be made by notice (“the direction notice”), stating the date the notice was issued, to—
(a) the employer and the employee if condition A is met;
(b) the employee if condition B is met.
In your situation, I would suggest that you clearly satisfy condition A because your EDI procedures enforce "reasonable care" and, if there was any error, it was is good faith, because you trusted the EDI transactions sent by HMRC. I suppose it could equally be argued that Condition A and the whole of regulation 72 does not actually apply because you cannot be expected to take reasonable care if you are not given the information in the first place. However, regulation 72 gives HMRC the powers to transfer the liability for the tax underpayment to the employee.
The following regulations (72A onwards) provide further rules on notices and appeals. I can provide you with text of those regulations if you need them.