Forget the routers that the ISPs provide. They are terrible and vulnerable (...mirai worm, DNS changer and other nasties)
The YouView box seems like a separate problem. Sounds like they're trying to sort that.
If you find certain devices are not connecting to your router (Wi-Fi access point) yet other devices are fine, then it doesn't sound like it's a line issue.
I would recommend putting Wi-Fi anlyser on your smart phone and checking to see whether there are many Wi-Fi connections contending with yours. You can also see what type of Wi-Fi signal strength is available in different parts of your home. Resolving your Wi-Fi issues could be as simple as moving your Wi-Fi onto a less congested channel. I find I have to do this dance every few months to ensure optimal Wi-Fi connection in furthest reaches of our home. If the 2.4 G spectrum is congested, a dual band router will at least give you the choice of 2.4G and 5G band - the 5G band as yet tends to be less congested.
If it's just the case the Wi-Fi signal doesn't penetrate the walls in your home very well, or your home is too large, you might consider a second Wi-Fi access point, connected to the existing router ideally via Ethernet Cable (Cat 5e/6) or if they work, Powerline adapters to shunt packets over your electrical wiring. They don't always work and there are always security risks with doing this - neighbours might be able to sniff traffic from your network for instance.
If you still think your Internet might be the issue, you can always connect a device directly to the router using a Cat 5e/6 Ethernet cable and run whatever tests you like. Personally, I like to run mtr from a linux box to 8.8.8.8 (to Google's DNS Servers) but if you run Windows, could at least open a comand prompt (Windows key +R, "cmd", <enter key>) and then type "ping /t 8.8.8.8" and press <enter>. Look out for any dropped pings. <ctrl> + <c> will stop the continuous pings (1 a second) and give a summary of results. With each ping, you should have a round trip time (latency) of < 45ms.
If you are a Mac user, then you can open a terminal and just type ping 8.8.8.8 <enter>. No need for the "/t".
(A ping is a single packet sent to another device. When that device receives it, it sends a packet back. The results will show whether any packets are lost and how long the round trip usually takes. Ideally on an ADSL connection, this should be no more than 45 milliseconds. Don't be afraid to open a command prompt and try this out. It will give some indication of your broadband connection quality..)
You can also run speed tests, but be aware that speedtest.net (ookla) is really only a good test of your circuit as the test servers used are only a few hops away. Try the thinkbroad band speed test instead, it's a little more realistic:
http://www.thinkbroadband.com/speedtest.htmlI hope this helps.
Unfortunately with TalkTalk, it takes quite a lot of patience to get results with them. I spent every other evening on the phone to them for months and although the line was fixed, we moved to Virgin Media for the main connection (effectively FFTC) and a new aDSL provider for backup. The aDSL is still shocking - connection is lost and resynced at least once each day and I've had to downgrade the connection from ADSL2+ to ADSL to ensure a reliable connection. I've not got the energy to take it up with the new ISP - I suspect the line is corroded somewhere and TalkTalk / OpenReach for all their investigations couldn't locate it. ...well to tell the truth, the termination of the connection in the cabinet was corroded, badly reterminated and then reterminated again. That at least got rid of the crackle from the line and stopped it disconnecting us for hours on end.
It seems with TalkTalk, you need to be at least capable of diagnosing the problem yourself - whether it's the Wi-Fi, the router, the line or something upstream.
Good luck.
Let us know how you get on. I might be able to offer further help if needed.