Holders of the Same sex partner visa who have continuously resided in the United Kingdom for a period of 5 years will quality for Indefinite leave to remain. You may apply using the SET (M) form.
If you were granted your same sex partner visa prior to the 9th of July 2012, you can apply for settlement after a period of 2 years of continuous residence in the UK as a same sex partner. However for applications granted after that date, you will need to wait till you complete 5 years on the route before you can apply for ILR. Please note also, that you will still need to meet the financial requirement to be eligible for ILR; except you fall under the exceptions as specified under Appendix FM