Has any restriction been put on the title register in his favour requiring his consent to sale? Your solicitor you used when you bought should be able to provide you with all this information or can download a copy of your title register from here for �3.00...
http://www.landregisteronline.gov.uk/
One option would be to get a valuation of the property by a local agent (bear in mind that this is not necessarily what it would sell for) and work out the costs which would have to be deducted (also allowing for any legal and agent's fees and tie-ins with any mortgage such as early repayment penalties) and work out whether it would even be viable to sell or try and buy the other out.
If the mortgage is quite new, there is a discount period and with the state of the current property market you would need to check whether everything could be paid off for a either a sale or for a transfer to the other and mortgage/remortgage to be feasible.
If you could buy him out then would you be able to get a sufficient mortgage on your own?
Another option would be to see if the council wanted to buy it back.