Yes, you should be getting much better than 15Kb/sec, but not necessarily better than 150-200Kb/sec at peak times. The problem is quite typical of a new connection to an ISP - any ISP - but from the description you appear to have some particular problems. I have just switched my line to Virgin from a BT business broadband line provided by my former employers. I had 3 weeks of high volatility while the exchange and server equipment tried to work out an acceptable balance between line speed and signal quality. Now it has settled down with a router indicated speed (i.e. attempted connection speed) of around 7000Kb/sec, which is somewhat higher than BT's estimated maximum speed for the line of 5500Kb/sec. For info, I live in a very rural area with poor quality copper wire patched several times from exchange via pole line to the house. However, the indicated speed is no guide whatsoever to what you will get end-to-end.
Your comment about achieving 15Kb on internet access vs speed tests of 150Kb are a non sequitur. Both will be affected by the level of contention for the servers concerned as well as any effects on the broadband line. The 150Kb/sec speed is eminently believable at peak periods, particularly during the line testing period, but do be aware that popular sites such as ZDnet themselves start to 'drown' at peak periods, especially when US subscribers come online too.
The key parameters will most likely be your line quality between exchange and master socket (and distance from the exchange is only part of the story) and the contention ratio between subscribers and ISP/exchange link. All the main retail ISPs use a 50:1 contention ratio, so at worst you may be getting only one-fiftieth of the potential speed indicated by your router connection speed (assuming everyone actively communicates simultaneously). By contrast, business broadband operates typically at a 20:1 contention ratio. I can relate personally to the difference in these ratios since, on the former business line, the line speed was always faster than my current Virgin connection now is at peak periods (BT was around 800Kb/sec; Virgin gets 250-400Kb/sec between 7pm and 11pm typically). In contrast, the Virgin connection achieves over 5Mb/sec effortlessly in the wee hours of the night when I'm probably the only person surfing via our country exchange.
I repeat that ALL the ISPs work on the same contention ratios, so changing ISP will likely achieve little, unless you find an ISP which is particularly unpopular on your exchange! Whether these contention ratios are reasonable, given the rapid take-up of broadband is another story altogether....
Your router connection speed suggests that your phone line is of poor quality, since the ISP will set up the connection speed to attempt the fastest speed possible before signal-to-noise ratio becomes unacceptably high. My router, for example, will cope down to about 6dB before it drops the connection and, as noted the indicated connection speed is around 7000Kb/sec. It may be worth trying some of the tricks suggested in other posts.