Peggy Mulvey of Chester (1851 census, b1776) was born in Satterthwaite, the Lake District, just ten miles from Lancaster.
This baptism might be Peggy, though this is not certain: 2 Apr 1775, All Saints, Satterthwaite, Lancashire, Peggy Smith - Daughter of Thomas Smith & Jane
Despite this being the female line, it might give a clue as to where the Mulveys came from.
In the 1851 census, William and Ellen Mulvey give their birthplace as Formby, however, we believe this is a mistake by the census enumerator, and it should have been the Lancaster village of Hornby.
Between Peggy, and William and Ellen, there appears to be a clear link between the Mulveys from Chester, Liverpool, Lancaster and Lake District.
It is likely they are all descended from Michael Mulvey, an Irishman, who married Margaret Roach on 31 Oct 1737 at St Michael and All Angels, Hawkshead, Lancashire. They had at least two children, James and Daniel, baptised on 14 Jun 1738 and 12 Feb 1740, both at St Michael and All Angels, Hawkshead.
Other records that might be relevant from Lancashire OPC:
Baptism: 25 May 1821 St Mary, Lancaster: John Mulvey - Son of William Mulvey & Ellen, born: 3 May 1821
Baptism: 20 May 1821 St Mary, Lancaster: Joseph Mulvey - Son of Margaret Mulvey, born: 25 Apr 1821
Marriage: 28 Sep 1828 St Wilfrid, Farnworth near Prescot, Lancashire: James Mulvey - (X), Pedler of this paris, and Ann Morgan - (X), Spinster of this parish, witness: Timothy Mulvey, (X); Peter Moss
Marriage: 18 Jun 1891 Christ Church, Blackpool, Lancashire: James Mulvey, 37, Painte, Bachelor of 4 Braithwaite Street, and Mary Ellen Moore - 28 Spinster of Carleton Terrace; groom's Father: John Mulvey, Spinner.
Baptism: 3 Sep 1837 St Patrick, Liverpool, Lancashire: Winifred Mulvey - Daughter of Robert Mulvey & Elizabeth (formerly Bond), born: 25 Aug 1837, godparents: Arthur Doran; Winifred Bond;
Burials at St Mary's, Lancaster
28 Aug 1800, Ann Mulvey - Dau of John Mulvey 30 Aug 1800, Elizabeth Mulvey - Wife of John Mulvey 4 Nov 1799, Joseph Mulvey - Son of John Mulvey 6 Dec 1799,Thomas Mulvey - Son of William Mulvey