No. It's on all plans. There is no web n walk tariff, it's just a ?1 data limit on all of them.
*Web 'n' walk terms and conditions
Compatible handset required. ?1 maximum daily charge applies to Mates Rates, Everyone and Text Appeal customers. Charges of 0.73p per KB applies until ?1 per day (midnight to midnight) is spent. If you have already spent ?1 and you browse for a continuous period from before midnight to after midnight, all of that period will be charged at the new day?s rate of 0.73p per KB. Not applicable to connection via CSD. Additional charges apply for use outside the UK.
Fair use policy applies. To ensure a high quality of service for all our customers, the web 'n' walk service is not to be used for other activities such as (but not limited to): modem access for computers, internet based video/audio streaming services, peer to peer file sharing, internet based video downloads and internet based telephony. If such use is detected, notice may be given, after which network protection controls may be applied which will result in a reduced speed of transmission.