Yes, texts are free to both you and your customer* when sending within the UK through the Working Feedback service. The texts are included within the Feedback Plus package as part of the monthly subscription of up to 1,500 total requests (both email and text) per month.
*If your customer has a Pay as You Go package, they may be charged by their provider when they click on the link, however that is not something we have control over and the customer may prefer to be contacted by email.