But officers at Bracknell Forest Council said that they thoroughly checked the tree in Longhill Park, Winkfield, for any signs of the lesser spotted woodpecker.
Wildlife enthusiast, Leanne Dawson, from Priestwood, Bracknell, said: "I go past that tree every day and hear the babies chirping. But then on Friday morning it had been cut down.
"They are protected birds and the council need to stop chopping down trees this time of year."
However, the council insists that the park ranger and tree surgeons that they hire are experienced and always check trees for nesting birds and that they were confident there were none nesting in what they considered a dying tree.
Richard Walton, Bracknell Forest Council's head of parks and countryside, said: "We have looked into the resident's concerns thoroughly and we are as confident as we can be there were no nesting birds in the tree.
"The contractor is very competent with many years of experience and followed clear guidance in regards to wildlife in these circumstances.
"The contractor carried out all the necessary checks before starting work and would not have begun work if there had been any sign of nesting birds."
The woodpeckers, which are about 100 times rarer than their relative, the greater spotted woodpecker, tend to make their nests in the holes of dead or dying trees.
A spokesman for the Royal Society Protection of Birds said: "The lesser spotted is a protected species which has suffered an amazing and astonishing decline in recent years.
"During breeding season our advice to councils and residents is to minimise the amount of cutting of trees.
"If you have to cut them down check that there are not breeding birds in the tree and protect yourself from breaking the law."
The council said that the trees in the area where Miss Dawson said she saw the woodpeckers posed a risk.
Sue Boyce, spokeswoman for the council, said: "As a rule we wouldn't do that this time of year, but the trees were dead and dying and deemed to be dangerous as they were hanging over a path."