You are at 'liberty to apply' to court for enforcement. Ultimately the court can sign the papers for transfer and payment of the debt can be enforced like as with any other debt - a warrant of execution, a third party debt order; a charging order; or a judgment summons.
It is possible to represent yourself, court officials will tell you the correct form and can help by checking if you have filled it in correctly. However, in these cases it is usual for a costs order so parties not adhering to the court order can expect to be ordered your legal costs. If you use a solicitor the other side's fear of paying the penalties in costs often resolves matters.