Replacement router

My router was supplied by Talk Talk and it's on network DSL 2640R, whatever that means. I've been having trouble with a slow broadband and was wondering if I replace the modem what sort would I have to get. Talk Talk wants £50 for a replacement router. On eBay they are not expensive second hand but some are shown as being 3780 not 2640. What does that number mean? Would I have to get a Talk Talk router if I stay with Talk Talk or would say a BT one or any other be ok? The purpose is to see if another router would solve the slow broadband problem. Does this sound like a sensible thing to do?

DSL is the type of connection it is, DSL uses the phoneline, and is what you need...

The "2640R" is just the model number..

Honestly though, if you're out of your contract term, your ISP will usually send you a replacement router (while restarting another 12 months)

but any "ADSL/ADSL2+" router should do...

Thanks, Ghozer. I'll try to convince TT to replace the router. When her broadband went slow one of my neighbours managed to get BT to improve it. They had to repair a connection that was up a telegraph pole. I suppose my broadband could be suffering in the same way? Anyway, I'll also try to get TT to have a look at the incoming cable. Last time I tried this they told me to plug the router into the test socket that's inside the BT wall plate where the cable comes in. But the plug on my router cable doesn't fit because it's intended for plugging into a telephone filter unit which has the square DSL socket whereas the BT test plate has the normal telephone socket behind it. But I did plug the router into this DSL socket, ie the filtered outlet right next to where the BT line comes in and the broadband didn't get any faster. So I came to the conclusion that the problem with my slow speed is either the router being of old design or the BT incoming line has a fault. Does this make sense to you? I don't know anything about being at the end of my contract term I'm afraid but I will ask.