Stained glass windows at St Michael and All Angels, in Bedford Park, have been vandalised just days before the church's 42nd annual festival.
The four windows, which were nearly 100 years old, were damaged on the night of May 25.
Inspector Manpreet Bins of Hounslow police said the person who smashed the windows must have thrown something at them "with considerable force."
He said: "Thousands of pounds' worth of damage has been caused and the windows were smashed beyond repair."
Father Kevin Morris, vicar of St Michael and All Angels, said: "We were deeply saddened at the malicious damage done to our stained glass windows, which have been part of our church for nearly 100 years and also for the perpetrators of the crime. It is hard to understand why they did it."
Spokesman for the church Torin Douglas said although police said the windows were damaged beyond repair, St Michael's was still examining whether they could be repaired.
The 42nd St Michael and All Angels Bedford Park Festival starts this weekend with a fortnight of arts and community events being staged in and around the church.
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