This is the information I have found so far: Albert Woolley (your grandfather) bapt 11 December 1870 together with his twin brother Arthur at St Stephen's Church. The family were living at the time in Brass Street. Thomas was a sword cutler*.
Lydia Margaret's father was Thomas Shelley and he was living with the family in 1911.
Albert's parents were Thomas Woolley and Hannah. I believe they may have been married in 1892 but will have to re-check that.
Thomas Woolley was baptised at St Alkmund's Church, Derby on 4 September 1836. His parents were Charles Woolley and Mary Clews.
The family moved to Birmingham sometime before the 1851 census and can be found living in Brasshouse Passage (off Broad Street). Charles was working on the canals at the time I believe.
Thomas had an older brother, also born in Derby, named William Henry. William Henry had a son named Samuel who was born in 1869. Samuel was Albert's cousin. Your Dad and my Mom, Doris Lilian, were second cousins so that makes The Baron and Lady Penelope third cousins! Exciting or what?
* In the 18th century there was a famous sword maker in Birmingham called Woolley but I've yet to find a connection.