The router is establishing the pppoe connection to the exchange (WAN side), and then passing it on (wired and wireless) to your devices, giving each device an appropriate local IP address (LAN side).
If you only have one device and want it wired, the device can do the pppoe connection (as your laptop did during test). A wireless access point could probably do some or all of the LAN side work. It might not be able to doll out the appropriate IP addresses. It probably won't be able to do the WAN side pppoe connection. If the access point can do all of that, it is just an alternative router, which you can use ok.
Options: You could use your own alternative router. You could unlock the modem and get it to do the pppoe connection and DHCP, and use a suitable wireless access point.
As Dr Saffron says, the wireless may be bad anyway. You could install inSSIDer on the laptop. That will help you sort out the best channel, and the best position for the wireless router (be it the TalkTalk one or an alternative one).
Moved (with trepidation) to BT Infinity 2 for upload speed. Happy BE user for several years.
Edited by StephenTodd (Wed 14-Nov-12 13:39:14)