Update has broken access to all admin pages

Latest update was applied along with an update to admin_menu module after both appeared as available updates. An error was generated but I did not copy that message, not expecting a major problem. However I now cannot access the majority of admin pages - modules, administrator, people, reports and more and get an error message 'The website encountered an unexpected error. Please try again later.'

This was true when using the admin menu but is also true if I try to getaround using URL www.aspergillus.org.uk/admin

Thus far I have not noticed any problem with the web pages themselves (including edit, display) - just admin pages

I have turned off the admin menu and it makes no noticeable difference - still get same errors when I try www.aspergillus.org.uk/admin

Next 2 suspects: AT update (applied 10/1/2015) and the update system itself

I can trigger the following message if I try to run update.php via the URL www.aspergillus.org.uk/update.php

PDOException: SQLSTATE[22001]: String data, right truncated: 1406 Data too long for column 'filename' at row 1: UPDATE {system} SET info=:db_update_placeholder_0, filename=:db_update_placeholder_1 WHERE (filename = :db_condition_placeholder_0) ; Array ( [:db_update_placeholder_0] => a:19:{s:4:"name";s:8:"AT Admin";s:11:"description";s:144:"A better admin theme for Drupal 7. Clean, calm, invisible. Includes left and right sidebars, Overlay support and all AT's theme setting goodies.";s:4:"core";s:3:"7.x";s:10:"base theme";s:13:"adaptivetheme";s:7:"release";s:7:"7.x-3.x";s:6:"engine";s:11:"phptemplate";s:10:"screenshot";s:250:"sites/all/themes/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/at_admin/screenshot.png";s:11:"stylesheets";a:1:{s:6:"screen";a:1:{s:16:"css/at_admin.css";s:252:"sites/all/themes/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/at_admin/css/at_admin.css";}}s:7:"regions";a:11:{s:7:"content";s:12:"Main content";s:13:"sidebar_first";s:13:"Sidebar first";s:14:"sidebar_second";s:14:"Sidebar 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[:db_update_placeholder_1] => sites/all/themes/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/at_admin/adaptivetheme_admin.info [:db_condition_placeholder_0] => sites/all/themes/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/adaptivetheme/at_admin/adaptivetheme_admin.info ) in system_update_files_database() (line 2269 of /home2/asperweb/public_html/modules/system/system.module).
The website encountered an unexpected error. Please try again later.

I found a similar thread here: https://www.drupal.org/node/1602312 which suggests that the update system may be at fault but this is not the same situation so I want to ask for advice before trying the solution described there.

I can restore the website as it was on 9th using backups (and will have to shortly as we cannot wait long!) but would prefer a solution which would help if I see this again!

Thanks