Case won with costs? What happens next?
Step one is to try and agree the costs. Usually, the starting point for that is a schedule showing the work done and time spent, but if that fails, a formal bill of costs will be required, which needs to be served within three months of the date of the costs order (CPR 47.7). The winner then has a further three months to start proceedings for detailed assessment, that is to say the formal quantification of the costs by a judge, assuming that the paying party has served objections to amounts claimed by formal points of dispute (CPR 47.14). That is what the CPR says, but in any sensible world, what the protagonists should do before that stage is reached, is to consider Alternative Dispute Resolution, the most well-known form of which is costs mediation (see Alternative dispute resolution versus having your day in court: another round to ADR (Part 2)).
