Waiting time(days)for Landlord Action to file for accelerated possession

How many days the Landlord Action company(on Open Rent) take to file court claim.

For the legal review, before charging £1599 the waiting time is almost 15 days as compared to other legal companies. My notice periodgiven to tenant ends this week. As the end of legislation is nearing; I have asked them if caseworker can file court claim next day but so far no reply .

I dont want to wait for another 2 weeks to go to court. Anyone used Landlord Action before?