In the meantime, to get you started, a list of baptisms for parents named Thomas and Elizabeth.
Christ Church, Spitalfields
30 May 1814; Thomas Read; Thomas & Elisabeth; Wilkes St; weaver
02 Oct 1814; Elizabeth Ann Read; Thomas & Elizabeth; Wilks St; weaver
27 Feb 1820; George Read; Thomas & Elizabeth; Wilk's Street; weaver
12 Feb 1836; Elizabeth Reed; Thomas & Elizabeth; Artillery Street; labourer
St Matthew, Bethnal Green
02 Jun 1822; Ann Read; Thomas& Elizabeth; Wilmot St; weaver; born 31 Mar 1822
06 Feb 1825; James William; Thomas& Elizabeth; Wilmot St; weaver; born 18 Dec 1824
11 Nov 1827; Jane Read; Thomas& Elizabeth; Wilmot St; weaver; born 03 Sep 1827
17 Jan 1830; Charles Read; Thomas& Elizabeth; Wilmot St; weaver; born 23 Dec 1829
14 Jun 1835; Alfred Read; Thomas& Elizabeth; Wilmot St; weaver; born 22 May 1835
14 Jun 1835; Benjamin Read; Thomas& Elizabeth; Wilmot St; weaver; born 22 Jan 1833
St Leonard, Shoreditch
21 Nov 1813; Sarah Read; Thomas & Elizabeth; Duke Street; turner
14 Apr 1816; Thomas Edward Read; Thomas & Elizabeth; Duke Street; turner?
03 Mar 1818; Harriet Read; Thomas & Elizabeth; Long Alley; turner
07 Jul 1822; Caroline Read; Thomas & Elizabeth; Union? Crescent; turner
16 Nov 1823; Elizabeth Read; Thomas Henry & Elizabeth; Union Crescent; ivory turner
25 Oct 1830; Ann Reed; Thomas & Elizabeth; Whitmore Road; dissenting minister; born 01 Jan 1827
25 Oct 1830; John Reed; Thomas & Elizabeth; Whitmore Road; dissenting minister; born 05 Oct 1828
25 Oct 1830; Martha Reed; Thomas & Elizabeth; Whitmore Road; dissenting minister; born 17 Sep 1830
05 Aug 1833; Nicholas Reed; Thomas & Elizabeth; Holywell Lane; clock maker; born 08 Mar 1832
18 May 1834; William Read; Thomas & Elizabeth; Swan Yard; clock maker
Holy Trinities, Minories, Tower Hamlets
21 Oct 1838; Thomas Read; Thomas & Elizabeth; 49 Church Street; porter; born 27 Sep 1838
21 Feb 1841; Ellen Read; Thomas & Elizabeth; 49 Church Street; porter; born 22 Jan 1841
St John, Hackney
08 Nov 1818; Henry Benjamin Read; Thomas Charles & Elizabeth; ?; appraiser
30 Aug 1829; Thomas William Read; Thomas Charles & Elizabeth; Duncan Place; commercial clerk
St Botoph, Aldgate
29 Oct 1843; Ann Read; Thomas & Elizabeth; 5 Little Somerset Street; porter; born 06 Aug 1836?
29 Oct 1843; John Read; Thomas & Elizabeth; 5 Little Somerset Street; porter; born 21 Jun 1841
26 Oct 1845; James Read; Thomas & Elizabeth; 6 Chequer Place; porter; born 04 Oct 1845
02 Apr 1848; Mary Ann Read; Thomas & Elizabeth; America Mews Minories; porter; born 03 Mar 1848
01 Feb 1852; William Read; Thomas & Elizabeth; America Mews Minories; porter; born 08 Jan 1852
St Botolph with Bishopgate
09 Sep 1838; Thomas Peter Read; Thomas & Elizabeth; ? Place; clock maker; born 03 Aug? 1838
09 May 1841; Caroline Read; Thomas & Elizabeth; Newmans? Place; clock maker; born 31 Mar? 1841
04 Jun 1845; John Myatt Read; Thomas & Elizabeth; Newmans? Place; clock maker; born 09 May 1843
St Marylebone, Westminster
16 Jan 1825; Emma Read; Thomas & Elizabeth; Portland Town; trade; born 25 Jul 1824
St Thomas, Charterhouse, Islington
29 Mar 1850; Eliza Read; Thomas & Elizabeth; 4 Thomas Court; clock maker
26 Feb 1854; Elizabeth Ann Read; Thomas & Elizabeth Ann; 5 Portland? Place; florist?;
St Andrew, Holborn
12 Dec 1813; Thomas Reed; Thomas & Elizabeth; Cross St; china man
St John, Hoxton
27 Feb 1850; Augusta Amelia Reed; Thomas & Elizabeth; Bachus Walk; plumber & glazier; born 15 Apr 1848
All Saints, Battle Bridge, Islington
01 Apr 1855; William John Reid; Thomas & Elizabeth; Rodney Street; plumber
St Margaret, Westminster
26 Jul 1816; Thomas Wotton Reed; Thomas & Elizabeth; Cannon Row; lath render; born 26 Jul 1816
17 May 1818; Ann Reed; Thomas & Elizabeth; Cannon Row; lath render; born 07 Feb 1818
29 Jun 1823; Eliza Reed; Thomas & Elizabeth; Cannon Row; lath render; born 18 Apr 1823
St Martin in the Fields, Westminster
12 May 1817; Thomas Reed; Thomas & Elizabeth; 22 Pouton? Street; glass man
St Marylebone, Westminster
27 Oct 1818; Alfred Reid; Thomas & Elizabeth; -; wade; born 13 Jun 1818
St Mary le Strand, Westminster
15 Jan 1820; Sarah Read; Thomas & Elizabeth; St Mary le Strand Poor House; tailor; born 12 Dec 1829
St Clement Danes, Westminster
02 Aug 1824; Thomas Henry Read; Thomas & Elizabeth; 53 Stanhope Street; tailor
08 Apr 1828; Caroline Rebecca Read; Thomas & Elizabeth; 6 Clement Lane; tailor