My answer is based VHG on a same sex couple and I believe PP is correct.
JBW, you do not mention a dissolution order and if you wish to arrange this your civil partnership (cp) will have had to have lasted at least one year and you will have to show that the cp has irretrievably broken down and you have been separated for at least two years if you both agree or 5 years if you do not both agree.
You will both have the right to live in the home and if the mortgage is in your joint names you are both jointly and severally liable for the entire payments, not 50%, I have assumed no children are involved. I would suggest you try to agree with your ex cp how the finances are split up, preferably in an amicable fashion, if you are unable to agree an assessment process will take place and you may be in the hands of the court. You should see a solicitor as soon as is possible with the full information that you have available.