You can take an action for Specific Performance of the contract, your solicitor will advise. Even the threat may be enough to encourage them, but as others have said, if you can come to an arrangement that would be satisfactory to both parties, that would be ideal.
How would you feel if the issue was in their favour? If you stick it to them, they could let you commence proceedings and drag things out for a few months before relenting and closing, negating most of that gain for you in additional legal fees.