Please see below the verbatim message received from HMRC and taken from BIFA website:
If a business deregisters for VAT, any Economic Operators Registration and Identification (EORI) number(s) they hold will also be removed at the same time.
EORIs are needed for authorisations, including a UK Internal Market System (UKIMS) authorisation, and licences. To continue using these there are actions a business needs to take:
Authorisations (including Duty Deferment Accounts and guarantees) – contact the supervising office. This can be found in the authorisation correspondence received originally.
Licences – to continue using these please contact the issuing government department
If a business still needs an EORI number, they can apply for a new GB EORI number. The number is usually confirmed immediately. Once a business has a GB EORI, they will then be able apply for an XI EORI number, if needed and they meet the relevant criteria. The number will be issued within five working days of applying.
If a business needs help getting a new EORI number, please contact HMRC.
General, HMRC