it's the slowest point that determines the speed, your previous connection as 1Mbit was 120k/s, so that was not the slowest point - so changing that would have made no difference
most users (like, you for example) have much slower upload speeds than download, so they can't send anywhere near as fast as they can download - on telewest you have 0.38Mbit to upload at, so someone else with a 0.5Mbit connection couldn't download from you at full speed
that is often the limiting speed in most cases, most of the time the other user has 256k upload so you'll get 30k/sish from them, which is why the most common speed to get is that, no matter what your maximum download speed is - it will only help to upgrade it if you are actually using it in the first place, which would normally mean downloading a lot of files all the time
btw Telewest are a good choice, only ISP I would use except perhaps BT (but BT charge more) because i really want reliability and none of the others come close to it, been with them years (must be at least 4 or 5) and only had it go down a few of times and those have almost all been short 10 minute outages at like 5am (and I've been using it as it went down every single time - lol), once a few years ago it was slow for a day due to them breaking something before they got redundancy in place, a few months ago it was off for a few hours because someone tripped over something (that's what it normally means when they say equipment failure, they are referring to the engineer), and the other week something broke and took them off all night but that was at the same time that a power surge fried my network so i didn't notice it (i bet they were related... their surge protectors just as broken as mine?)