Extended payments of HB - rent increase

A client has been awarded an extended payment of HB after they came off ESA and went into work. During the 4 weeks of the extended payment their rent increased however the extended payment continue to be paid at the previous rate.  The local authority have said that they will not increase the extended payment to take into account the new amount of rent. 
While the amount of extended payment is normally based on your entitlement in the week before you come off benefits and go into work, CPAG handbook seems to suggest that you can be paid a higher amount if your circumstances change and subsequently your entitlement increases, (pages 254-255). Would the rent increase not be seen as a relevant change of circs?