I am dismayed but not altogether surprised at just how difficult this is proving to be. The clues were there from the outset - HMRC's Agent Services Account very similar in name to the HMRC Online Services for Agents.
What I have found out, from getting through at last on an online services general helpline (note the helpline number included in the letter with my Activation Code for my new ASA was actually a string of letters), was that, despite what the aforementioned letter says, the login itself has to go via a different route. If you go in through the usual route, but with your new login details, you'll be taken to a "limbo" account. No clients (despite my having linked them previously), but I was able to add a service and request an authorisation for a client). The helpine told me to go to www.gov.uk, then in the search box type in Agent Services Account, and login with my new details. This worked - although the only screen I am offered is one inviting new authorisations, or the option to link clients (which I tried in case my previous attempt had failed - however the message confirmed that I have previously linked - although where are my clients?).
Update - whilst typing out the above, I have received an HMRC Online Services Account response to my emailed query which I sent immediately prior to creating this post - I shall have a stab and return. In summary though, it advises "access your account again, making sure you are not using a bookmarked/old link to access your login screen. We have made several changes to our site recently and so any saved links you have been using may no longer work correctly. Please close all your browsers down and use the link below (the link allows you to sign in as well as register) and not a favourite or bookmarked page. The link given is https://www.gov.uk/log-in-register-hmrc-online-services"
To be continued..................