Hi Alan,
We do a lot of this work for clients all over the world - I've just been talking with one of your colleagues this morning.
One of the big "red flags" here is that you are still running Moodle 2.8 which has been out of support for over 2 years and contains a number of known security issues that could allow a malicious user to compromise your site. (hopefully these security issues aren't being exploited on your site and are causing some of your performance issues!)
Moodle 3.1 and higher also come with PHP 7 support which shows some very big performance gains.
Quite often we find sites that have not had configured the Moodle cache correctly - make sure you have a read through:
https://docs.moodle.org/28/en/Caching
Also make sure you have php opcache running
Those 2 items (php opcache and MUC configuration) can make some very easy/significant performance improvements on your site. But if you already have those configured there are other things we can suggest.