See Castle Street East 1 to 15 & 11 Berners Street (in London Addresses dataset)
Alexander Robertson Land Tax 1780-1784 2 Castle Street East / SunFire 1794 Alexander Robertson, 16 Castle Street, Oxford Market, tailor
There were quite a few Alexander Robertsons around and it may just be coincidence that the two above were both in Castle Street. No Robertson appeared in Castle Street Land Tax lists in the 1790s so the insuring tailor above could have been a sub-tenant at Castle Street East or West., though East was perhaps more likely as John Gibson paid Land Tax at 16 Castle St East from 1796 and John Gibson tailor was insured at 16 Little Castle St in 1798, and premises often hosted succeeding tenants in the same trade. Even the tailor can't be identified clearly as there were several Alexander Robertson, tailors around in the 1810s and 1820s (from occupations in baptism records), though there was perhaps only one master and the others were journeymen. The para below makes a pretty story of adoption anyway.
Alexander Robertson taylor & habit maker SunFire 1786 Little New St, Shoe Lane (Holborn) / 1794 insured at Castle St as above / 1796 Alexander Robertson tailor of Bedfordbury (Covent Garden) voted Fox & Horne Tooke / 1802 ditto voted Fox & Graham / 1807 piece broker & man's mercer 25 Bedfordbury victim of theft oldbaileyonline / SunFire 1819 tailor 3 Angel St, St Martins le Grand / bapt 20.11.1820 St Andrew Holborn Rosetta, illegitimate, supposed to be born 1805, parents not known, adopted by Alexander Robertson, tailor of Christchurch, Newgate St (near to Angel St) / SunFire 1824, 1828 tailor of 3 Falcon St, Falcon Sq / will dated 24.9.1846 of Alexander Robertson tailor and lodging house keeper formerly of Falcon St but now of 158 Aldersgate St mentioned adopted child Rosa Robertson aged about 40 who "lived with me and my late wife" over 30 years will proved PCC 4.1.1847 / Elizabeth Robertson of Aldersgate St age 72 buried 25.9.1833 St Botolph Aldgate / Rosa Robertson 1851 directory 158 Aldersgate St commercial boarding house / 1851 census Hampstead Rosa Robertson age 42 born Cheshunt, Herts, cousin of Joseph Stone carpenter age 35 born Brentford, Middlesex / 17.6.1854 William George Bodily widower tailor of Rupert St, Liverpool married at St Botolph Rosa Robertson spinster of Falcon St, father John Lloyd deceased / Rose, dau of John Lloyd & Lucy bapt 10.2.1809 Cheshunt, Herts.
I found these baptisms, father Alexander Robertson tailor, mother Mary, of Drapers Bldgs Shoreditch 25.8.1818, Little Bell Alley Coleman St 30.8.1819, St Botolph Bishopsgate 1.6.1826, mother Jane St Martins Lane 5.2.1824, mother Eliza, Huish Court St Ann Blackfriars 21.1.1827. No baptisms found of Alexander & Elizabeth Robertson earlier, tailor or not