ISTR▸ , that this or something VERY similar has been discussed previously on this forum.
A member in receipt of jobseekers allowance reported considerable problems in obtaining the card, the staff in the job center seemingly being very reluctant to authorise this.
That would have been me then! And what a palaver it was getting one.
As can be seen in the thread grahame linked to, the JobcentrePlus Travel Discount Card is also available to Employment & Support Allowance (ESA) claimants if they are actively engaged with a work coach with a view to returning to work at some point, or if the are planning to do, or are doing, what is called 'Permitted Work'. Such ESA claimants would usually be those who have been placed in the 'Work Related Activity' group. Those in the 'Support' group would be unlikely to be eligible for the Travel Discount Card as they don't have to engage with a work coach.
Back in 2014 when I applied for mine i was both seeing a Work Coach on a monthly basis and doing some Permitted Work.