The browser problem is now solved.
Waited a few days after Addthis was uninstalled, went back to WP plugins over the weekend, downloaded the latest Addthis version and it is working OK so far now. Disabled WP-Super Cache at the same time but no idea whether that was causing the problem.
At the moment am able to add custom service codes into the dialogue box to customise the plugin but nothing happens. No custom plugin appears on our site. Have opted for one of the custom default options. Not a big issue.
Also now get the update post error that others are reporting with the Yet Another Related Posts plugin – YARPP – that disappears when YARPP is disabled.
Have the latest WP version installed and all plugins are up to date.