The £25 per month Sports offer currently on their website is available to existing customers who are billed directly through NOW themselves and not a third party such has BT TV for example.
You will need to be have less than 30 days remaining if on an existing Sports offer or not have a Day Sports Pass active or saved on your NOW account.
You would need to discuss that with BT TV themselves.
Some people on the Community Forum have a BT TV Membership for example Entertainment or Cinema and a second account for NOW Sports.
This is a pain though, where you would need to keep logging in and out of accounts when watching NOW on TV Memberships across both BT TV and NOW direct.
There is one thing that really appeals to me with BT TV using their BT hard drive Youview box is that you can record live NOW channels (including NOW Sky Sports) which you can't being a NOW direct TV member.
Another bit of advice is that this offer comes with one month free Boost.
If you don't want the Boost features and pay the extra £5 per month charge in the second month onwards then cancel the Boost Membership during sometime in month one a few days before the Boost will be charged against your account.
I don't know what BT TV Sports package deal you are currently on and what price you are paying for it, but if you do cancel your Sports package with BT TV, then just be aware in the UK the NOW Sky Sports package is just the 11 number Sky Sports channels and you won't have the live channel record facility like on your BT Youview box.
If you have both the BT Sports and NOW Sky Sports BT TV package, then i would have thought it would be cheaper or on a par staying with BT TV.
Another downside on using NOW direct that i find is that NOW Sky Sports on Demand is limited to 25fps and it takes an age for the live Sports events to be added to their service and if you are thinking of watching Premier League games on Demand there is a possibility this season you won't get the full games replay and so far it's looking like around 25 minutes highlights only.
This is where the BT recordable Youview box has it's advantage being a BT TV customer using the NOW Sky Sports service.