There is a Thomas Driscoll who appears in the 1871 Census in Poplar, London. He was 9 years old at the time, which would mean he was born in 1861 or 1862. He was born in Poplar, but his father Daniel Driscoll was born in Ireland. The wife is not listed, so it's hard to say if she wasn't at home when the census was done or whether Daniel was a widower at this time. Looking at the census document itself, it looks like he is listed as a widower, but it is not that legible. There is another Thomas Driscol listed in England who was born in the right time period, but his parents were born in England.
Here's the info on the one from Poplar:
Name: Thomas Driscoll
Estimated birth year: abt 1862
Father's name: Daniel Driscoll
Where born: Poplar, Middlesex, England
Civil Parish: Poplar
Ecclesiastical parish: All Saints
Town: Tower Hamlets
Registration district: Poplar
Sub-registration district: Poplar
ED, institution, or vessel: 24
Household schedule number: 357
Page Number: 18
Daniel Driscoll 44
Mary Ann Driscoll 11
James Driscoll 2
Thomas Driscoll 9
Ellen Driscoll 17
Eugene Driscoll 15
This is the citation. It's from Ancestry, but I'm sure you could find it on Family Search too:
Class: RG10; Piece: 585; Folio: 27; Page: 18; GSU roll: 824897
Ancestry.com. 1871 England Census [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.
Original data: Census Returns of England and Wales, 1871. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1871. Data imaged from the National Archives, London, England. The National Archives gives no warranty as to the accuracy, completeness or fitness for the purpose of the information provided. Images may be used only for purposes of research, private study or education. Applications for any other use should be made to the National Archives, Kew, Richmond, Surrey TW9 4DU.