Wayne,
You need to collect up the facts bit by bit.
If you can find Richard and Mary in 1911 then that will tell you how long they have been married for and then you can probably find the marriage in FreeBMD. The marriage certificate will give you her maiden name and the names of the couples fathers and occupations.
Altenatively you can guess that the couple were probably married about the time of the birth of the eldest child and thus locate the marriage in FreebMD.
You can also get the birth certificate for any of the children to find out Mary's maiden name.
Find Richard PARKER in 1871 and then in 1861. Leaping back to 1851 could get you on the wrong track.
You have Richards age so you may be able to get his birth certificate. Then you may be able to find his parents marriage, If it is before 1837 then try Familyearch
https://www.familysearch.org/It takes time and a little money. The telly program "Who do you think you are" makes it look easy but some paid researcher spent weeks and a fair bit of cash to do the background stuff and they do not show you that.
Bryan
PS
You can use Familysearch later than 1837. You can see the baptism of George Henry PARKER in Hartlepool and this may be the marriage of his parents:
groom's name: Richard Wharton Parker
groom's birth date: 1847
groom's age: 25
bride's name: Mary Jane Sayers
bride's birth date: 1852
bride's age: 20
marriage date: 26 Aug 1872
marriage place: Southwick, Durham, England
groom's father's name: Richard Wharton Parkes
bride's father's name: William Sayers
groom's marital status: Single
bride's marital status: Single
indexing project (batch) number: M01318-2
PPS
Wayne - ask your local library whether they have a subscription which will give you access to the 19th Century Newspapers
Newcastle Courant Friday 7 November 1851
Deaths -
In Church Street, on the 30th Ult., William, infant son of Mr Richard Parker, chemist.