Bits & Bytes
One thing that might explain some of the difference is that the 56k Eircom refer to is 56 kilobits / second.
Internet Explorer, as far as I can recall, specifies in kilobytes / second, where 1 byte = 8 bits.
So when IE says 4k/s, it means 4 kilobytes/second, which is 32 kilobits/second, which while still not great, is within shouting distance of the 56 kilobits/second Eircom are promising.
The 56k is also a theoritical maximum, based on line quality, distance from exchange, your modem, and other variables.
Finally, I would take the Eircom demo with a pinch of salt, as that's all it is, a demo.
Regards,
Philly