What 'certified refurbished' actually means here
Microsoft's own refurbishment programme is reasonably well-regarded. Units are inspected, cleaned, and come with a warranty, typically 90 days to a year depending on the seller. That's not nothing. But 'certified refurbished' sold through Amazon third parties is a looser term than you'd hope. Check the seller name and warranty terms before clicking buy, because the certification quality varies considerably.
The financial case for buying refurb
New Series X consoles sit around £449 at major UK retailers. At £372, you're saving roughly £77. Over, say, three years of use, that's a modest but real difference. If you're replacing a last-gen Xbox, the upgrade jump is substantial: 4K 60fps gaming, much faster load times, Game Pass compatibility. The refurb route makes sense if you're price-sensitive and comfortable with a shorter initial warranty window.
For someone buying their first current-gen console, a lightly used refurb is often indistinguishable from new after five minutes of play.
Where it gets complicated
The Series X as a hardware category has one known annoyance worth mentioning: it runs warm and the fan can be audible in quiet rooms. That's true of all Series X units, not just refurbs. What refurbs add is the question of how hard the previous owner pushed it. You can't know that.
No included game, likely no original packaging, possibly a shorter cable. Small things, but worth knowing.
Who should actually consider this
If you'd buy it new anyway and this saves you £70+, it's a reasonable gamble with a verified seller. If you're already unsure about the investment, the refurb uncertainty probably doesn't help your case.