Whenever a court makes an order for costs to be assessed by a detailed assessment it should consider making a further order that a sum on account of those costs should be paid out straightaway. Indeed, the rule (CPR 44.2(8)) expects an order to be made unless there is a good reason not to do so.
A request for an interim costs certificate may be made once a request for a detailed assessment hearing has been filed with the court (CPR 47.16(1)).
There is no specific provision in the rules for a payment on account of costs to be ordered after the order for costs was originally made but before a request for an interim costs certificate can be made. A party wishing to apply for an interim payment on account of the costs to be assessed needs to make an application in accordance with CPR Part 23 (see Section 20).