The £20 discount is only on the specific EE One tariffs, it doesn't automatically apply to your current plan, especially as you already had a 6 Month Half Price promotion.
If you get in touch with EE Customer Services or try to upgrade through the App, you may be able to choose one of these plans going forward.
If you are in contract and don't upgrade or change your mobile deal, the only immediate benefit you receive for taking EE Broadband alongside Mobile is an Unlimited Data Boost to all plans over £10pm on your account. This obviously isn't too beneficial when you already have Unlimited Data.
Depending on your price plan and upgrade eligibility you may not be able to change to an EE One plan until the last 45 days of your existing contract, or by upgrading to a Flex Pay plan with a new device.
You can find out more about EE One and what it means for you on the info page here: https://ee.co.uk/ee-one
I would advise talking to the Upgrade team on 150 to check your options.
