Can't access any gmail accounts due to an authorisation error 400:invalid request

I have three gmail accounts which have all stopped working on my iMac. This is the error message:

Error 400: invalid_request

You can't sign in to this app because it doesn't comply with Google's OAuth 2.0 policy for keeping apps secure. You can let the app developer know that this app doesn't comply with one or more Google validation rules.

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• redirect_uri: urn:ietf:wg:oauth:2.0:oob

I'm running macOS Sierra on a 2011 iMac

This problem is specific to my iMac and does not affect my iPhone 7+ running 15.8.1

I did come across an article a while back which involved setting up an 'other' account and then renaming it - I can't find that article and even if I did the gmail account I fixed has now stopped working. In addition to that, the option to choose 'other' when adding email accounts now lists a further list of mail account types whereas before it opened up a generic set of entry fields. Choosing to add a gmail account triggers the same error message.