NHSE have produced an updated communications pack which includes some text that you may wish to adapt for your organisation and letter templates to support in managing common queries from patients, which can be adapted for other communication channels.
There are also additional resources for GPs on the COVID-19 Vaccination Booking Service and Vaccination Centres here.
Public Health England’s Campaign Resource Centre has lots of materials to communicate the progress and delivery of the COVID-19 vaccines which can be used to help increase take up of the vaccinations.