The Trust was founded in 1862 by London-based American banker George Peabody, who in the 1850s had developed a great affection for London, and determined to make a charitable gift to benefit it.

[4] The Peabody Trust was later constituted by Act of Parliament, stipulating its objectives to work solely within London for the relief of poverty.

It cost £22,000 to build, and contained 57 "dwellings" (i.e. flats) for the poor, nine shops with accommodation for the shopkeepers, and baths and laundry facilities on the upper floor.

Rents were to be paid weekly and punctually; there was a night-time curfew and a set of moral standards to be adhered to; and the dwellings could not be used for certain trades.

Peabody states that in pursuit of its mission it will: "help people flourish by providing great homes and services and making a positive impact in communities."

[9] However, the consultation has been controversial, as the ballot conducted in March 2020 asked the 'yes' or 'no' question: "Are you in favour of Peabody's proposal to include Lesnes Estate in their regeneration plans for South Thamesmead?".

In March 2011, Peabody raised £200 million on a corporate bond, at a rate among the best secured by a housing association borrowing in its own name.

[31] A number of complaints have been made against Family Mosaic in the national and local press, including heating being cut-off for five months of the year,[32] a ceiling collapsing,[33] poor administration at one of its care homes,[34] and a rodent infestation.

[35][36][37] In 2014, Family Mosaic took the unusual step of apologising to its tenants after a malfunctioning computer system led to an increase in complaints about its repairs service.

[38] In February 2022, the body of Peabody tenant Sheila Seleoane was discovered in the hallway of her flat, with the Coroner later concluding that she had collapsed and died in August 2019.

During this period neighbours tried repeatedly to raise the alarm regarding a putrid smell and maggot infestation without success while Peabody, who were aware that Ms Seleoane had not paid her rent since August 2019, started taking rent payments out of her Universal Credit benefits in March 2020 and cut off the gas supply to the flat in June 2020.

[39] In June 2023, The Housing Ombudsman made a finding of severe maladministration in respect of Peabody, relating to its failures to properly deal with reports of anti-social behaviour and noise nuisance, which led to a resident terminating her own tenancy to escape the situation.

[41] Since taking over much of Thamesmead in 2014, Peabody have demolished large parts of the Lesnes Estate, including Binsey and Coralline Walk.