Who When Where

Could it be Clonrush or Clonmulsk -- a civil parish in the barony of Leitrim, now in County Clare, Ireland.

Further, the wife of the head of the household in Philips Street is a Frances Taylor - yet to be confirmed but when Thomas married Jane Susannah in 1826 one of the witnesses was a Frances Murray so it's possible Ann is in the home of her daughter. The woman living at Phillips Street, Kingsland Road...

In 1841 Eliza is with her parents in St Mary's, Islington (sorry no street noted but probably Paradise Place) and a live-in servant in 1851 (details missing). In 1841 Eliza and parents are living at Lee's Court, Elder Walk . Where is she in 1851? (As regards the 1841 census link, jonwarrn did that ...

Norfolk Nan wrote: ↑29 Nov 2023, 16:25 ...horsekeeper was added to the entry so I think someone else was the informant...

Sorry, I'm not seeing that on the actual image. The image I see says just "cab-driver". Birthplace: Middlesex.
Also, can I just confirm if Eliza's father is named Robert...or is it Richard?

Because a cab driver was a steady profession. Most cab drivers stuck with it, and didn't do various labouring jobs (as your James did). You'll need to trace the James Murray (cab driver) after 1851, to confirm if it's another person.

As mentioned earlier, Charlotte may have been in service by 1841. She would've been the right age at the time (about 16). Or she may have died. Too young to have married by 1841. As for James in 1851, I'm having doubts the fellow in Paddington is him. You'll need to research it a lot more. You said ...

Do you have the address where Eliza's first daughter was born in 1853?
NOTE: Paradise Place and Elder Walk were near each other at the time.

...but that suggests, I think(?), that the Thomas Murray+Jane Susannah Parsons couple aren't the pair in the 1841 census. That marriage took place in 1826 and that Thomas was a widower. Yes, I think we can safely say that is a different Murray family (the one with Jane Susannah Parsons). You can ru...

Using jonwarrn's latest settlement record(s) find this could be the Ealing marriage for Thomas & Jane:

10 March 1805 - Ealing
Thomas MURREY & Jane POWNEY
Jas SIMMONDS & Sarah POWNEY (looks like the Powney sisters married on the same day)

Where is James in 1851? Have you located him yet?
Also, who are his wife's parents? Where is Eliza in 1841 and 1851? When did she hook up with James?