Well if your WiFi is going to need expanded coverage and you've only got £100 then you're limited in choices. 5GHz doesn't travel great distances, especially through walls. If that 4m drop off is in another room that's not hugely surprising. 20MBps is 160Mbps which seems a tad slow but it does depend on your device and other variables. What speed do you get if you wire it in?
I think if you're going to have people move in and need improved coverage (as well as speed) then you're probably not going to solve that with a single replacement router as already mentioned.
For that budget I think I'd probably buy a Tenda 3 node mesh system, turn off the Wifi on your current router and then introduce the mesh to see if it improves. Buy it from somewhere easily returnable and it is low risk. It will then be transferable to your Virgin router or whichever ISP supplied router with whomever you go with. I've no personal experience but your budget will stretch to two Honor Router 3s which could do the same and experiences on here suggest they are very good indeed. If correct then it'll almost certainly be better than the Tenda I suspect which IME is "OK" for a regular household but maybe not for heavy users and gamers/streaming.
Another option, though dependent on layout of your house and construction materials, is you may find better performance by instead of mesh, letting a centrally placed Access Point somewhere on your landing ceiling handle WiFi duties. Same principle in that you stop your ISP router doing WiFi and let something else take care of it. This would need you to run an ethernet cable from your router to the placement location though. And a decent 4x4 access point like a Ubiquiti NanoHD is going to be 50% more than you want to spend. You do get pretty graphs with it though
Unless you want an improved experience solely in the room your router is in (or very close) then I don't think there's an all-in-one that's going to help. If I've made huge assumptions and it is only the room you're in you worry about WiFi then one Honor Router 3 and a modem will probably suffice. That's £20 for a BTOR modem off ebay and £50 I think for the router. May not have the graphs though.
Can you elaborate more on how the wired connection suffers when there's a lot of WiFi devices? Are we talking high latency or limited internet bandwidth available or something else? What speed is you current Plusnet connection rated for? Since you can get 160Mbps over WiFi, and assuming you are on FTTC, then I would I be right to also assume you have a need to transfer things around your network too (otherwise even with those poor WiFi speeds you're more than enough to saturate an FTTC connection and the problem isn't your WIFi or router - it's your internet connection speed and what you're asking it to do) ?
