The introduction of the Marriage (Same-Sex-Couples) Act 2013 legalised same-sex marriage in England and Wales. Civil partnership ceremonies can still be performed for same-sex couples but carry different legal rights and obligations. More information can be found on the UK Government website.
If you wish to have a civil partnership ceremony, the process is similar to a civil marriage, but you will need to mention you want a civil partnership ceremony when you book Registrars and at your legal notice appointment.
Couples in a civil partnership can have it converted to a marriage (retrospectively) with or without a ceremony.