There are a number of potential causes.
Most likely is there is a issue at the exchange, often caller ID can stop working when you move ADSL (broadband) providers.
Do you have any other phones which are still showing caller ID, so we can rule out a phone line \ talk talk issue?
You suggested you have already been in contact with Talk Talk and confirmed Caller ID is still enabled on your account, if you havent spoken to them and just checked the portal it may be worth a call to them to ask them to double check the service is enabled, and the exchange correctly configured (they may have migrated your line to newer equipment without your knowledge. and mistakes do happen).
Im not sure about Talk Talk but I believe you should be able to dial *#234# ***** it should confirm if Caller ID is enabled at the exchange for your line, however if you get an unobtainable tone it just means Talk Talk dont have this auto test facility enabled.
In terms of the phones them self, you could try and use a different ADSL filter which plugs between the phone and the telephone socke (if you have broadband on the line).
Next we could look at the phone \ base station config, the manual for your phone can be found here.
First go into Menu and select "Handset Setup", then select "Time settings", then select "Time Adjustment" then set "Caller ID" to "Auto"
Next in "Handset Setup" check to see if "Auto Talk" is set to "Off"
Other than that there arent any other settings on the phone which would enable\disable caller ID, which would then leave something wrong with your line, the first thing to do is go round and unplug all the phones, routers and modems you have connected to the phone line, switch off the base station and turn it back on once its plugged back into the phone line. Place a test call to your landline and see if caller ID is now working, then one by one add the phones \ modems \ routers back ont he line and see at which point the fault develops.
Out of all of this, my money is on Talk Talk having an issue at their exchange.
Please let me know how you get on.