Been off flying for a few days, but when I checked, the UK National Airspace System was receiving plans from IFPS and automatically inputting them in to the NAS Flight Data Processing system within 2 minutes of the time the plans were showing as being filed with IFPS. This system feeds data to all the UK Area Control Centres and many of the large airfields. These were plans with no errors or things which the UK NAS system didn't like.
For plans which requires some manual intervention in the UK NAS system, they join a queue, so their turnaround time will depend on how many other plans are ahead in the queue for correction. This number is usually quite low, less than 10% of all plans submitted in to the UK NAS system if I recall.