See here for info on Perk and what it can be used on and the limitations:
https://ee.co.uk/why-ee/perk
The discount will apply to SIM Only or the Airtime component of a Flex Pay agreement (not the device cost). If you are not eligible for Flex Pay, I believe it can be used on 24 Month Device Plans with a single bundled price but within the restrictions included below (no Upgrade Anytime plans).
It is not eligible to be used on any promotional or time limited offers, only on EE's core pricing, which may be what you're referring to when you state "the most expensive plans".
From "The legal bit" at the bottom of the EE Perk page:
"The discount: The 20% discount will only apply to the price plan’s monthly recurring charge and will last for the duration of your minimum term. At the end of your minimum term, your price plan’s monthly recurring charge will revert to the usual pre-discount price, unless you upgrade again using a new EE Perk code.
Non-eligible plans: You cannot get the discount if you are on a plan that includes an annual upgrade benefit. The discount cannot be used in conjunction with any other offer or discount. It is not available with Family & Friends, 10% Multi-line, early upgrade discount, Good as new devices, or any wearable device."
