I received an invoice with a due date in the past, is it valid?

IANAL and I don't live in the UK, so I can't speak to specific UK law.

But just speaking from common sense: You imply that the invoice is for a valid expense. At least, if they were billing you for some work they never did or that you never agreed to, I presume you would have brought that up rather than just talking about the dates.

In the US, it's not uncommon for an invoice to have a date after the due date if it is not the first time you were billed. If, say, someone did work for you in, say, January, then typically in early February they will send you a bill saying it is due in late February or early March. If you don't pay, then in March they'll send you another bill saying it's past due. So the March bill may be dated March 11 but show a due date of March 1. This is totally ordinary on a late bill.

If the very first bill they sent you was mailed after the due date, you may or may not have some argument against being required to pay late fees. If the bill is legitimate -- if they really did do this work and you agreed to this price -- then you should certainly pay the amount of the bill. You might dispute late fees based on the dates, but that's not grounds to dispute the original bill.

As I say, I don't live in the UK and I don't claim to know UK law. But I would be very, very surprised is a court were to rule that you don't owe for a legitimate service because someone made a mistake and put the wrong date on a bill.