Broadband ofcom code - delayed activation compensation

Hello.

I recently switched my broadband service from talktalk to BT. Unfortunately there was a delay in activating my service with BT by almost 3 weeks! I thought, having read up on the new ofcom code that BT is a part of, that I would be entitled to £5 a day compensation for each day I was not receiving broadband. So as inconvenient as it was for me to not have broadband - I sometimes work from home and this was impossible with no internet! - I was consoled by the thought that I would be adequately compensated.

Fast forward to my service finally being activated with BT, and instead of confirming the compensation I thought I was entitled to (£5 X 20 days delay = £100), they have said I'm only entitled to £20! Because apparently while my broadband was delayed, they had my landline working fine after 4 days! I don't even have a home phone - I didn't ask for a landline, it is just part of having broadband. But BT say that because part of my service was working after 4 days im only entitled to 4 days compensation. I feel a bit swindled, and that this great publicity of a 'broadband guarantee' all the companies are harping on about is actually a bit of a sham.

Does anyone know if BT are right about this or whether I should argue with them a bit more over it?

With thanks in anticipation!