@ThePBW
Assuming that you are on ADSL or FTTC (i.e not on a full fibre FTTP product), you need a land line in order for you to be provided with broadband. Therefore, excluding any call plan packages etc, there are two elements to your bill, broadband and line rental. Plusnet may well have set the line rental element to zero but your broadband element will be subject to the price increase. The price increase applies to the net prices of your products, that is the prices after discounts are taken into account.
If you are getting a price increase of £3 as you suggest, this would imply that your existing monthly bill is around £21. If your line rental is zero then the increase in that element will be zero, but the increase for a broadband element of around £21 will be around £3. Note, if you have referrals, that the increases apply to your bill before the deduction of any referral discounts which are unchanged.
I recently received my email from Plusnet setting out my price increase. Assuming your email is similar, the actual increase is set out in the first paragraph but within the "What's Changing" coloured box below there is an example of how prices will increase set out for three products at notional prices which will not reflect you particular circumstances.
