Presumably all your speed tests so far are using your own router , rather than the supplied BT one , then it’s not unreasonable to expect you to disconnect it and replace it with the BT router , even if it’s only for a short period whilst a few tests are performed, if the issues remain, it suggests that there is an underlying issue , obviously if the speed is only poor using your own supplied router it isn’t really your ISP’s problem.
Connect the BT hub and run new speed tests , also post the (BT) router connection statistics
I would run their test. I think that’s fair. But the reason I got a 3rd party modem was cause I had issues with BTs to begin with. And when the technician came like 2 weeks ago we tried both. He saw that the router was getting 68 but speed tests at my laptop were only getting 20
Remember to use an Ethernet cable from your PC/Laptop direct to the router with nothing else connected to the router, and with WiFi disabled.