In the first instance borrow or steal a long ethernet cable and run it through the house to see if that resolves the issue. If it does then you could try powerline adaptors to get wired ethernet to the Xbox. Their speed depends on your house’s wiring but they are usually pretty good.
TP-Link TL-WPA4220 TKIT 2-Port Powerline Adapter WiFi Starter Kit, Range Extender, Broadband/WiFi Extender, WiFi Booster/Hotspot, No Configuration Required, UK Plug https://amzn.eu/d/iY962Lm
If they are no good you can return them. Ive recently put a TP Link Deco X50 mesh in my parents house and that works really well. Wifi is strong and fast everywhere now.
If I may expand on Jobys excellent post, get the 1GB versions as the 600 series only has 100mb ports, so the interplug mesh will be 600mb, but you will only ever get a max of 100 out of the ethernet port.
WiFi wall plugs are essential if you want to carry WiFi signal around the house with no fuss, especially if you have thick walls. Although it relies on electric cables so they also have to be in good condition to carry signal.
I mostly disagree with the above advice, they work quite well for lower performance solutions…web browsing etc. Any kind of device that serves as a relay, unless possessing something like a dedicated back-haul, will slow a wireless connection. Powerline stuff, I’m not that familiar with, but it does need to be on the same circuit to function well.
The most obvious source of lag is actually the on the router (QoS/double NAT?)/traffic, or the traffic going through it. 13MB uplink isn’t that great, so a device like a camera or streaming activity would quickly strain it. This is completely ignoring anything like Discord/video that might be open with the game stream.
I would recommend you check what router you have, see what the traffic uses are and if any settings can be tweaked to bias the XBox. Failing that, invest in a better router. They’re actually very competitive compared to things like Powerline or WiFi “Boosters”, I would consider both these two solutions the worst possible items to increase or stabilise coverage.
If you want something rock solid, a good router when combined with Mesh package, can support very high levels of coverage for a pretty low cost and without cables. If you’re happy to run CAT cable, Access Points and a router is the way…this is getting into nerd territory though.
Just to complete, I assume your connection is ADSL from the stats you mentioned? Additional checks on the line would be good to to see if the connection is consistent. Check a filter is fitted…the router is in a sensible place, not overheating etc.
There are plenty of second hand router options available on Gumtree/EBay. Just make sure what ever you’re doing involves routing and modem as one action, for instance, do not get a high performance router and connect it to your existing hardware without disabling its router function.
PS. Same for Mesh systems. DecoMesh, BT…there are loads of fairly decent ones to be had.
One of my neighbours who demolished and refurbished his place only a few years ago has last month broken open the walls again, pulled ethernet, and made good - because both him and his kids are into gaming and wifi just wasn’t cutting it.