The Family Court in England and Wales may make any order in respect of the costs of litigation it thinks just. This is enshrined in the Family Procedure Rules 2010 ("FPR") at Rule 28.1. As such, it is perfectly permissible for a Judge to order that one party pays (in full or in part) the costs of the other party. In civil proceedings, this is usually done on a "costs follow the event" basis (i.e. the losing party pays the costs or some of them incurred by the successful party).
However, in "financial remedy proceedings" in the Family Court, the general rule regarding costs is that each party is responsible for paying their own costs. This is commonly referred to as the "no order as to costs" rule and is set out in the Family Procedure Rules 2010 ("FPR") at Rule 28.3(5).
Not all proceedings in the Family Court which relate to financial issues are "financial remedy proceedings" for the purposes of Rule 28.3(5). For example, an application seeking an order for Maintenance Pending Suit (i.e. payment of maintenance by one party to the other on an interim basis pending the final decision as to the financial outcome of a divorce or dissolution of a civil partnership) does not fall within the definition. Therefore the general "no order as to costs" rule does not apply to such proceedings and each party is at risk of a costs order being made against them.
There are also cases which fall within the definition of "financial remedy proceedings" where the Court decides that, although the "no order as to costs" regime is the starting position regarding costs, a costs order is "appropriate…because of the conduct of a party in relation to the proceedings" per Rule 28.3(6).
Examples of such conduct/behaviour may be a failure to meet one's full and frank financial disclosure obligations; a flagrant disregard of the FPR or an order of the Court; or pursuing an application where all the facts point to the chances of success being hopeless.
In 2019, the President of the Family Division (MacFarlane P) amended Practice Direction 28A at paragraph 4.4 such that the Court will view issues of conduct broadly and will generally take the view that a refusal (or by definition, a failure) to negotiate a settlement openly and reasonably would be considered conduct about which the Court may make an order for costs in financial remedy proceedings.
Since then there has been a growing willingness by the Family Court to do just that with Mr Justice Mostyn (the National Lead Judge for the Financial Remedies Courts within the Family Court in England and Wales) in the vanguard of this movement (e.g. see OG v AG  EWFC 52 and JB v DB  EWHC 2301).
Earlier this month, in a case reported as LM v DM  EWFC 28, Mr Justice Mostyn arguably went a step further in this regard. The proceedings were for Maintenance Pending Suit, interim maintenance for the parties' children and for a legal services payment order. None of these proceedings are defined by the FPR as being "financial remedy proceedings" and therefore the "no order as to costs" rule did not apply. The Court could therefore make any costs order it felt was just.
However, rather than simply deciding whether an order for costs was appropriate and, if so, the amount of cost to be paid by the losing party to the successful one, Mr Justice Mostyn made a costs order in favour of the successful party but reduced the award by 50%. Although the case was "clearly a win for the applicant" (§2) they had "made no serious attempt to negotiate openly and reasonably" (§3), leaving the impression that the applicant was "determined to fight the application come what may" (§3).
Whilst Mr Justice Mostyn was able to make whatever costs order he saw fit, it is notable that he imported the obligation to negotiate openly and reasonably into non-financial remedy proceedings, thus suggesting it will be treated as a firm requirement for all parties engaging the Family Court no matter the type of proceedings involved. In Mr Justice Mostyn's words at paragraph 4 of his very short judgment in this matter, "Litigants must learn that they will suffer a cost penalty if they do not negotiate openly and reasonably".