Matthew married Maria Mason in 1836 in Deane, Lancs but she died of typus in 1839 aged 23. They had one daughter, Hannah Maria Barton, b 1837 d 1888. She married Alred Barlow in 1876. In 1881 he was a retired cabinet maker. There were no children.

From Matthew's marriage to Mary Alexander (nee Wigan) there were five children:

1. Mary Dean 'Minnie': b 1848 d 1917 she married Thomas Ratcliffe Ratcliffe-Ellis in 1868. Thomas was knighted by George V at St Jame's Palace in 1911 for his services to mining. They had eight children.
2. Elizabeth 'Betty': b 1849 d 1909 she married Thomas's brother, William Ratcliffe 'Billy' Ellis in 1882. They had three sons.
3. Anne 'Annie' Wigan: b 1851 she married James Howard 'Jim' Walker in 1874. They had seven children.
4. Matthew Henry T.: b 1854 d 1902 in 1881 he was a cotton salesman. In 1901 he was living with his sister Eva, unmarried as a steel agent.
   
5. Eva Jane: b 1856 Wigan lived until she was at least 90. Never married.