Order as to costs: explanation needed

IANAL, but I think it means the loser pays the winners, costs, but if the two parties don't agree what costs are reasonable, then a court order is needed to enforce payment of said costs?

Legal costs is a complicated subject. When a case is decided and order is made about who has to pay whom the costs, which is what happened in the case you are involved with. In your case the claimant has to pay costs to the defendant.

No liability to pay any money arises until the amount of costs has been quantified. This can be done either by agreement between the two parties or by a further court process to assess the amount of costs payable.

In your case, there is a further step, which is that even when the amount of costs is established, that amount is not payable until the court has considered the matter again and decided whether the sum agreed or awarded for costs should be paid.

When I won a case the judge simply asked me what my costs were. Being rather good at preparation I had them all written down; I read them out and he added them to the money due on the spot.