I'd recommend buying an NAS drive, where you can store all your media for easy access. This will connect to your network, and let you access the video files from all around the home.
Once you have a competent media-file setup, you needn't store all the data directly under your telly! The next step would then be to add something small to your TV that can access it. I'm fairly sure there's a ton of Android boxes which will do that, but I'm not sure which would output 4K. You'll have to look into that.
In fact, your TV (if it's a "Smart TV") might already be able to natively access a "DLNA" media server. (Most NAS drives contain DLNA support, and will happily stream videos to whatever asks for the files)
There's also the Apple TV 4K, but you're looking at just under £200 for that alone. I recommend it due to it's ability to access all the tons of apps, be they games or media, but .. yeah, not exactly the cheapest method!! (Oh, and the remote's a bit pants)
But definitely look into getting an NAS media setup working, first. It'll help you a ton in the future, you can use it for backups, and you'll free up all that space on your computer, too!!