Arbitration is a form of dispute resolution in which the parties appoint an arbitrator to adjudicate their dispute and make an award which is legally binding. It can be used to resolve financial matters, and in some child matters. Generally it much quicker than contested hearings via the Family Court. However, unlike court applications for which you just pay an initial court fee, you have to pay for arbitration, which can cost a few thousand pounds. Both parties have to be willing to attend arbitration.
More info can be found from the Institute of Family Law Arbitrators - ifla.org.uk/