I've just left TalkTalk (having been with Pipex since year dot only for Tiscali/TalkTalk to totally trash what was once a good ISP).
Whilst I agree with the other reply that said your line speed is affected by your line quality so in theory you shouldn't see any improvement in speed, I would say that you might see a difference in the 'quality' of your connection.
I moved from TalkTalk to PlusNet last week, and already I have seen my speedtests stabilise at 1.4meg whereas whilst on TalkTalk, it would fluctuate between 600k to 1.2Meg.
The line stats never changed, (Attenuation around 55 dB, Noise 12.6 dB) and what I mean about the "quality" is that TalkTalk often throttled, high ping times/latency.
Disconnects on the TalkTalk network happened daily and once every four weeks we'd have a 1-2 day outage (longest was 5 days).
Because of my location out in the countryside, I am never going to get massive speeds, and our exchange at Turgis Green is not LLU so we are at the mercy of BT equipment for most of the way.
I would advise about not going near TalkTalk if only down to the sheer numpty factor of their front line support.
They use 'overseas' support techs who have a script that they cannot deviate away from even if you give them solid evidence or even a history of a previous problem.
i.e. telling the support tech that you are logged into your router with debug diagnostics switched on, you can see the ADSL signal, can ping all the way to the first boundary router but then the network is dead. His first question, "Can you confirm that your PC is switched on". His second question, "can you confirm your router is switched on", his next statement was "it sounds like your computer has not been given an IP address by your DHCP so we will need to reset your router"
Every single time I would phone TalkTalk support it would take at least 30mins of going through their scripts before they would then admit they would have to raise it to Level 2 support. It would then take a maximum of 5mins once it got to Level2 support.
Quite often they would say they would raise a Level 2 ticket, but never did (they got penalised if they raised too many Level 2 tickets wrongly so often would say they had raised a ticket).
Anyway, I digressed, but in summary, you might not see a speed increase, but IMHO, moving to TalkTalk you will not experience a great 'quality' of your connection in terms of bad routing/shaping/lag/latency and absolutely [censored] support.
Plug your stats into this site: http://www.farina1.com/adsl/
and that will give you a rough indication of what you should expect.
It will be your ADSL Sync speed that will be the limited factor based on the Attenuation/ SN Margins you give. (You should be seeing 8Meg/20Meg download depending on whether ADSL/ADSL2)
ps. Apologies for any errors. It's way too early on a Sunday morning when I first began replying and this is my first reply on this forum.