It it legal to enforce collection of an (incorrectly) estimated tax bill

The HMRC guide on how to appeal against an HMRC decision regarding indirect tax (which includes VAT) suggests that the answer is yes, it is legal:

The tribunal will not usually hear your appeal unless the tax due as a result of the decision you disagree with has been paid.

In other words, you must pay up before you can have your appeal dealt with -- unless you show that it would cause you hardship:

But if you believe that paying the amount you wish to appeal against would cause you hardship you can ask HMRC not to collect the payment due until the appeal has been considered by the tribunal.

The general point is that HMRC will attempt to collect what they believe to be the accurate amount. It's your responsibility to keep them updated, to challenge their numbers if you think they've made a mistake, and if that doesn't work, to go through the review and appeal procedure.

In the case of VAT, the legal underpinning for using an estimated amount comes from the Value Added Tax Act 1994, where Section 73 ("Failure to make returns etc.") states:

(1) Where a person has failed to make any returns required under this Act ... or to keep any documents and afford the facilities necessary to verify such returns or where it appears to the Commissioners that such returns are incomplete or incorrect, they may assess the amount of VAT due from him to the best of their judgement and notify it to him.

and:

(9) Where an amount has been assessed and notified to any person under subsection (1) ... above it shall, subject to the provisions of this Act as to appeals, be deemed to be an amount of VAT due from him and may be recovered accordingly, unless, or except to the extent that, the assessment has subsequently been withdrawn or reduced.

My non-expert interpretation of this is that HMRC may assess the amount of tax due as they see fit, whether that's based directly on documents received, or is an estimate; and that assessment is the amount that is due (unless later amended). In other words, it doesn't matter whether their figures are estimates or not; unless you can demonstrate otherwise, you owe what they say that you owe.

never bothered to de-register for VAT

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On the HMRC (gov.uk) website it says:

"You must submit a VAT Return even if you have no VAT to pay or reclaim".

More details found here: https://www.gov.uk/vat-returns