The HPV vaccine used in the NHS vaccination schedule is Gardasil 9 and protects against 9 of the types of HPV that can cause cancer and genital warts for most people with just one dose.
A complete list of ingredients for the Gardasil 9 vaccine is given in the patient information leaflet (PIL). Further information is also available in the summary of product characteristics (SPC).
Further overview of the HPV vaccine is available on NHS.UK and you can find out more about vaccine ingredients at Vaccine ingredients | Vaccine Knowledge Project.