If your spouse has legal aid then their solicitors should notify you of this fact. Note that having legal aid does not necessarily mean that they will have no legal costs to pay. They may have a monthly contribution to pay towards their legal aid and they will have to repay their solicitor’s costs out of any money or property that they recover or preserve (this is usually referred to as the ‘legal aid charge’). If they recover or preserve an interest in the matrimonial home, then they will have to repay the legal aid charge when the home is sold.
The fact that your spouse has legal aid does not prevent the court from ordering you to pay all or part of their costs, and any such order would not be restricted to the lower rates that legal aid solicitors are usually paid. On the other hand, a legally aided person has substantial protection against costs orders being made against them, so that such orders are extremely rare. This can be seen as a considerable advantage for a legally aided person, particularly in negotiations, but remember that if the legal aid charge applies then it is just as much in their interests as yours to settle matters, in order to keep costs to a minimum.