There's an initial application fee and a further fee to apply for a decree nisi to become absolute. Both of these fees are quite small and, depending upon your circumstances, you might not have to pay them. (Whoever submits the application to the court has to make the payments).
There's some useful information here. (It's a multi-page document. Keep clicking 'Next', and follow the subsidiary links, to get all of the information):
http://www.hmcourts-service.gov.uk/infoabout/d ivorce/want/index.htm
Chris