I eventually after a lot of grief worked out that the problem is Mailchimp for Woocommerce, It was dramatically slowing the whole site down. After deleting it the site including WP Super Cache is running just fine.
Reviews of the Mailchimp for Woocommerce plugin pretty much all say the same thing. I.e. it is a major problem slowing sites down.
Thank you for your response. Other users of Mailchimp for WC might want to look at their page load times/
