Smoke coming from chimney into room

[wannabe logger]

Lit my stove last night and was none to pleased to see alot of smoke coming into the room through the seam of the plate that seals the chimney whilst letting the flue pipe through. So removed stove today and swept chimney and barely collected a tiny bucketful of soot ( after 2 years burning ) so was a bit baffled about it all. Next stop was the roof to peer down the chimney...... then the problem became apparent. The bird cage had once allowed a few starlings to make their home inside the chimney so i wrapped expanded metal around it and was confident that no bird could ever get through that. Today however i saw that the cage was completely sealed up with soot, therefore forming an airtight cap on my chimney..... no wonder i was getting soot in the room.