Your FTTP is really only delivering 50Mbps down and 10Mbps up. Do you mean FTTC by any chance - I suspect you do.
Your very slow connection could be down to all manner of things. I suspect the old desktop does have an Ethernet port. I would start by lugging the PC to the router (temp measure) and trying with an Ethernet cable first. If you are closer to your router you might also get a stronger WIFI signal. I expect the issue is the WIFI, the USB WIFI dongles are often not great.
Depending on the distance and construction of walls etc WIFI might not be workable solution at all. You have a few options to consider:
1) Use an Ethernet cable if possible - old technology but still the best....if often inconvenient....
2) Find a more central location for the router.
3) Better WIFI card in desktop.
4) Cheap mesh WIFI system - the Tenda ones are very cheap and work quite well.
5) WIFI extenders - never had much luck with these personally.....
6) Powerline adapters - very dependent on the specific house, wiring mains noise etc. I am not a fan but some people swear by them - and they have fallen in price considerably recently.
7) An additional wired access point closer to computer - an old BT home hub available for peanuts on eBay can be used.
As with most things it is a bit trial and error and it is easy to waste money on ineffective solutions. If you can borrow kit such as powerline adapters before buying then great.
Personally, after trying a number of options in the past, I have found that a mesh system was the only way I have gotten good WIFI around the whole house. My mesh only has two nodes - Tenda MW6 ones, and cost £60 from Aliexpress. The second satellite is hard-wired though. If you don't need above 100Mbps then the MW3 nodes might be cheaper.
There is also a WIFI speed test app on Android (well loads of them) but one in particular that I found useful. You use it in combination with a tiny server app on a Windows computer that is hard wired to the router. You can then run around your property testing WIFI speeds in different locations and testing different setups. It is potentially better than using a Broadband speed tester as you are just testing your network. In my case my WIFI is much faster than my broadband.