I am very happy to hear from you and I'm very happy to share what information I have. MAWDSLEY is quite a common name in the Liverpool area so I don't know if there is a link or not. My MAWDSLEYs were originally from the village of Halsall but the family had moved to Liverpool by 1834.
My great-great-grandfather was George MAWDSLEY b. 1811 in Halsall. Parents were William and Martha WOODS. George married Elizabeth HAIL Jun 9 1832. The couple had 11 children: William b. 1832, Cicely b. 1833, Thomas b. 1834, Martha b. 1836, Elizabeth b. 1839, Celena b. 1841, Ralph b. 1843, James b. 1847, Jane b. 1850, Richard b. 1851 and George b. 1853. All except William and Cicely were born in Liverpool.
Of that lot, Richard is my ancestor. He later married Margaret LEATHER. Richard is on the 1881 Census living on Clare Street, Liverpool and working as a portmanteau maker. They had at least 5 children: Thomas b. 1866, Elizabeth b. 1875, Ralph b. 1877, Margaret b. 1880 and Caroline (my grandmother) b. 1883.
Please get back to me if you see a link.