Cloudflare is not a CDN in the strict sense, however it has certain CDN characteristics by passively keeping some of your content within its proxy network.
If you say your server is in the UK and so is your audience, your gain in performance would be probably rather minimal. It does depend on how fast your server responds and on how well it handles concurrent connections, but assuming it is decently configured it should handle that without problems. Furthermore, if it wasn’t you’d still have issues even with Cloudflare as all non-cacheable requests will still hit the origin, though certainly the overall number of requests will be lower because of caching.
The other big question is if you have any traffic limitations as that is an area where Cloudflare’s cache could help keep that number “lower”.
If traffic is of no concern either, the only thing you’d really gain is the security aspect. First of all, your server address will be hidden*) hence that won’t be an attack vector. Secondly you’ll be able to set up your own rules to stop requests from reaching your server in the first place.
You need to take all these things into account before switching to Cloudflare. Cloudflare can improve performance and security but it will still require tweaking some settings and you won’t have a guarantee that things will speed up all that much as a lot depends on your site’s setup.
*) That is, assuming you change your IP address after switching to Cloudflare and not you do not expose the new IP address in any way (unproxied records such as MX or sending emails from your server).