Could I ask for a bit of advice…is there anything you know we can do to improve mobile speed fairly easily? A client of ours has noted a few reports which seem to flag up the site being slow (or poor) on mobile?
I think you may have installed the AMP plugin on other sites, is that the sort of thing I should be doing?
I will also be switching this site over to be hosted on WPEngine which I hope will help.
WPEngine is better than most for speed.
The ultimate hosting solution for speed though is to use SpinupWP on a UK-based Digital Ocean droplet. That’s where I host my clients and it flies.
AMP is definitely a good idea – but does require some testing. You want to have it turned on for as many types of posts (pages, posts, portfolio, etc.) as possible – but very often that will cause display issues on those data types. So it takes a bit of testing and finessing.
Speed wise I recommend (and can deploy for you) the WP Rocket plugin.
Bear in mind though those speed tests can be a test problematic where they give % scores. Here’s some more information on that:
WordPress SEO Expert