The Quarries Were Where the Green Bits Are Now

The Quarries were where The Felling green bits are now. That's not a guarantee but its a knocking bet if the green bit is in the middle of a built up area. 

If houses could have been built there they would have been. The big exception is the Oliver Henderson Park which could not be built on but not because of quarrying

The last working quarry in Felling closed in 1972. When they started is unknown but goes back at least to Roman times. In written records times, we can go back to
 1478 when "gryndstones" were quarried from under the Hayning (large wooded area)

Per Joan Hewitt (JH), not just a well versed local historian but the granddaughter of a quarry owner,  there was "a great sweep of carboniferous sandstone known as the Heworth Band".

In 1807 twelve separate quarries were listed in Heworth Chapelry rates book. 

The biggest was that of Richard Kell and Co and the last was that of Tate Brown & Co. (Brown being JH's grandfather)

The High Burn hole was very deep, water filled and dangerous, the stone of increasingly poor quality. In about 1948 a young lad drowned. The quarry finally closed in 1952.
After filling with Heworth Colliery pit waste it became Felling Cricket Club.

Felling Park is another obvious one. (Felling Park also had a colliery shaft, another reason for it not being built on)

Heworth Low Burn Quarry was worked on until 1970  and eventually became a cemetery
The Bankies was formerly a quarry as was the Windy Nook Nature Park