Cluster flies are most active in April and October. Rentokil make a very effective Aerosol that not only kills them on contact but has a residual effect on glass and frames that kills their friends too. They are parasitic inside earthworms during the larval stage and have an immature fly that looks like fruit flies as well as the bigger ones that are similar in size to house flies. They hatchout evey few days and seek houses to overwinter in, especially in South facing windows.
Block as many external cracks you can (not easy on the 4th floor) and spray a residual pyrethrum based insecticide around any voids you cant block.
Guess what I have been doing this week.