If you want to divorce your partner, you need to apply a divorce petition by filling form D8 and D8A if you have kids. You also need to pay £340 for filing a divorce.

Send the forms to the court, if your partner does not defend the divorce, you can request the court to issue a 'decree nisi' to move to the next stage. However, if your partner does not want a divorce, the divorce procedure may take lot longer and cost you more money. For more, check here.