Family search have the follow as a family.
All Baptisms in Newcastle Upon Tyne with the following parents, some of them also mention grandfather Peter Mellis.
William Thompson 1787
Isabella Mellis 1791
William Joseph Thompson 1813
Elizabeth Louisa Thompson 1815
Peter John Thompson 1817
Isabella Sarah Thompson 1818
Ann Esther Thompson 1820
Henrietta cecilia Thompson 1823
Stephen Octivous Thompson 1824
Monica Lavina Thompson 1828
Frederick Augustus Thompson 1826
Alfred Strachan Thompson 1830
Would need to check each NE out to confirm if they are relevant.