HDMI to USB adapters (digital media players) for old TVs?

[Yurakucho]

I am blessed with two old (2008?) TVs which can't play videos from USB sticks (one can play music and photos from USB sticks, one can't play anything from USB sticks at all).

Usually I just put USB sticks in a Blu-ray player and play videos that way - but it's starting to malfunction.

Instead of buying a new player/TV, how about an HDMI to USB adapter? Does such a device even exist? Presumably it would have to have its own menu screen built-in, given that the TV wasn't designed for playing videos from USB sticks. How about accepted video formats? And my TV remotes don't have rewind/fast-word buttons etc., so how would that work...?

There's one on Amazon for under £6. However, I'm not sure it's what I'm looking for - I think it's just to plug in a laptop etc., rather than USB sticks...

EDIT: Apparently the thing I'm looking for is called a digital media player, and all the ones I can see are unacceptably expensive. I don't want slots for SD cards and all this stuff, just a USB slot. Any recommendations?