Standard UK double-sockets are rated to provide provide up to 13A continuous draw (from either or both sockets -actual draw can be up to 20A or more). The PSU is rated to draw 5A-10A, as per the manufacturer. A 5A fuse will work - before it fails. And it will fail, but hopefully not during a BIOS flash causing the OP to brick his mobo, or in the middle of something else important. A 5A fuse is sufficient for many laptops, but not a desktop.
I can say from personal experience that there's a big gap between what you CAN do and what you SHOULD do. Aside from extensive past personal experience working with UK-standard electrical systems, my company currently provides sensitive and extremely expensive electronic systems to the UK MoD and other EU customers. As part of the contracting process, I have to vet all aspects of the systems for compatibility, including cables, chargers, adapters, inverters, transformers, etc., so I'm reasonably confident that the advice I'm giving is accurate, but you don't have to take my word for any of this - all of it is easily verifiable online through reputable technical websites. Google is your friend
OP - I encourage you to research it yourself, but I think you'll find the adapter I linked in my last post is entirely sufficient and appropriate for your purposes. It's also cheap, simple and reliable. If you opt for a different solution that also incorporates a fuse, I'd advise you to get one rated at 10A-15A (220V-240V), or if the fuse is not inside that range, replace the fuse with one that is. You'd be okay with a higher rated fuse, but if you're going to have it in connection, you might as well take advantage of it as an additional protective measure for your PC.