Under GDPR article 4 Personal information is:
any information relating to an identified or identifiable natural person (‘data subject’); an identifiable natural person is one who can be identified, directly or indirectly ...
If the subject's name IP address, and other identifying information has been deleted, and there is no way to connect or re-connect the internal ID to an actual specific natural person, then that ID is not "Personal Information" under the GDPR.
Under GDPR article 127 a data subject is entitled to:
obtain from the controller the erasure of personal data concerning him or her without undue delay ...
But if the data is no longer identifiable to a specific natural person, it is not "personal data concerning him or her" and no right of erasure applies.
Beyond that, the right of erasure only exists if at least one of the provisions of article 17 paragraph 1 applies. Art. 17 (1) (b) will apply if the original basis for processing was the data subject's consent, but not otherwise. Art. 17 (1) (c) will apply if the data subject objects, unless there are "overriding legitimate grounds for the processing".
Under GDPR article 6 processing can be lawful because the Data Subject has given consent (Par. 1 a) but also because the Controller has a legitimate interest in the data (1 f). It would seem that malignant a record of who was an officer of a club or organization would be a matter of legitimate interest and thus form a lawful basis for processing basic ID information, such as the name of the person, even over a request for erasure. However other personal, information not needed for such a purpose would still have to be erased on request.
So I think that retaining the internal member ID would be permissible in any case, but retaining the name would be permissible, even over an objection, to identify club officers.
After additional Information
The OP says in a comment:
Every year we issue a printed handbook to each of our members containing, amongst other things, a full list of members complete with member ID, name, address, phone, email etc. There will be thousands of these in circulation from past years from which I could re-attach my DB memberID. Obviously I cannot erase all of them! The ICO have told me members have to accept the continued existence of the handbook when joining and cannot expect that data to be erased. Does this change things wrt the database?
This changes mattes a bit.
GDPR Art 17 paragraph 2 says:
Where the controller has made the personal data public and is obliged pursuant to paragraph 1 to erase the personal data, the controller, taking account of available technology and the cost of implementation, shall take reasonable steps, including technical measures, to inform controllers which are processing the personal data that the data subject has requested the erasure by such controllers of any links to, or copy or replication of, those personal data.
Just who needs to be informed in this case is not clear to me. It is a good thing that only "reasonable steps" are required.
The existence of the handbook means that the member IDs can be easily re-identified by anyone with access to a copy. They are therefor clearly personal information. A valid request for erasure will thus require removing the member ID from anywhere that it is visible to users at least, and if possible from anywhere in the database. A new random member ID to link together the various records where the deleted ID is used, provided that they do not include PI, could be substituted.
I still think that retention of the member ID and name for a former officer of the club is arguably a matter of legitimate interest, and not subject to a request for erasure, under article 17. But that would not apply to an ordinary club member.
Given the existence of the information in the handbook, distributed in "thousands" of copies, there seems less point in anyone issuing a request for erasure under article 17. It might be a good idea to remind requester of this situation. Still a person might feel that an online DB is much more exposure than a handbook in print available only to those members who happen to have kept it. In any case, the right still exisats under the GDPR.