Complaint about state of entire block of flats

Maintenance

I own one flat in a block of twenty-seven flats.
On my recent inspection I noticed a huge deterioration in the standard of the maintenance of the grass surrounding the building and the communal internal areas were filthy (tins of ravioli spilled onto carpet along with other food waste), childrens toys and clothing on hallway floors, prams and furniture blocking communal landing to fire exit window (unsightly as well as fire hazard and Health and Safety hazard).
Please advise as to best course of action to get these matters made safe and hygenic. I intend to write to managing company but is there any other course of action that I should consider to get a speedy improvement in standards at this property?