Not possible without also transferring their half share in the property to you. That means that, unless they want to give you this share, you will have to buy out their share. See a solicitor and speak you your building society.
Is your income enought to raise a mortgage for the full amount? If not, your lender probably won't agree to the mortgage being transferred into your sole name.
Speak to an independent financial adviser about setting up a mortgage to transfer the property into your sole name and buying out your partner. Speak to a solicitor about setting up a separation agreement so everything is set in writing. This is a legal document that both of you would have to sign. Find out how much a solicitor would charge for this and the subsequent legal work for the mortgage. Remember, can you afford the mortgage repayments on your own??