I bought by Freesat 4K (Recordable) TV Box second-hand from someone else. Can I still benefit from/claim under the manufacturer’s warranty/guarantee?

If you can show that the Box is still in the warranty/guarantee period (i.e. through proof of original date of purchase by the first owner) and proof that you now own the box, then yes, subject to the other terms of the warranty/guarantee, you can make claims under the warranty.