Welcome to this user forum.
BT Plus is a VDSL connection not ADSL.
You may find that the terms of BT Plus, and the "keep you connected" promise, require you to use a BT Home hub, so they can remote access it, to see if there really is a failure, before they send you a mini 4G hub.
I assume you just have normal superfast broadband?
Any bottleneck is normally on the upload path.
The BT Plus does not specifically state that you must use the BT hub at all times but it does state that in the event of a fault and prior to BT sending a mini hub to keep you connected "We will then run diagnostics to check everything is okay with your line. This will involve a few online tests. We might ask you to turn your Hub off and on again, check wiring within your home, or unplug your devices".
In view of that I would suggest that you can use your own router but in the event of a problem you should reconnect the BT hub prior to reporting a fault.
This is pretty much inline with how things are are on all the BT Broadband packages.
See Terms & Conditions
As for VDSL routers that have some form of local network priority controls, prices start at about £40.
With careful configuration, you should be able to reduce the effect that other users have on your gameplay, however you cannot control what happens on the Internet itself, so its probably not worth spending too much money on a different router, in case it does not help.
Even if people are just downloading or streaming content, the upload path is still being used for flow control and performance statistics. This may be sent at regular intervals, which may explain the intermittent slow responses.