Hi Hugh,
So looking at your site you have two classic optimisations that can be done.
Firstly, after your run Google PageSpeed you should see the following at the bottom:
"Download optimized image, JavaScript, and CSS resources for this page."
Click that and download the zip file.
You cant then upload the optimised images, and even run it again (sometimes you can do multiple passes).
Alternatively you can use some of the plugins already mentioned, or other online tools, but I'd avoid additional plugins if you can, and Google's tool works well.
Obviously if your images aren't finalised, then you can do this when they are.
Before optimising images, make sure you're not scaling images, using images that are too large, and so forth.
Regarding the other common fix:
"Eliminate render-blocking JavaScript and CSS in above-the-fold content"
Firstly make sure you don't have uncessary plugins or widgets loading extra render blocking JS and CSS.
Also make sure your theme is of a high standard (lightweight and well optimised, without uncessary bloat and requests).
Then if you still have this issue, you can try a plugin such as the following:
https://wordpress.org/plugins/autoptimize/
You can look at the "inline all CSS" (easy) and “inline & defer CSS” (better) options, covered here:
https://wordpress.org/plugins/autoptimize/faq/
However, care should be taken with any such plugins as they can break your installation.
Watch out for plugin interaction or odd behaviour.
Lastly, you're currently hosted with 1&1 and for a pretty small homepage your website loads rather slowly.
This is indicated by the Pingdom load time and Google's consider fixing "Reduce server response time"
1&1 heavily market in the UK, but they're a German business, and your website is actually hosted on a server in Germany.
This means there's a greater distance between your UK visitors and the server you're on.
Google now takes performance into consideration for SEO, so there's a definite benefit to hosting a UK website on UK web hosting.
1&1 are also not well known for good service or performance.
I hope that helps.
All the best,
Dan