Because such homes are converted outside the normal planning approval process, applicants need not provide affordable housing or contributions to infrastructure such as roads, schools and health services, says the LGA.
The organisation, which used figures published by the Ministry of Housing, Communities and Local Government (MHCLG), says such PD rights are "detrimental" to local communities and should be scrapped.
Its findings show that, since 2015, 30,575 homes in England have been converted from offices to homes without requiring planning permission – about 17,500 in 2016/17 and 13,000 in 2015/16.
This amounts to about eight per cent of all new homes nationally, according to the LGA. But it says that in some parts of the country, the route has created around two-thirds of new homes.
The LGA calculates that office-to-residential PD conversions accounted for 73 per cent of new homes in Stevenage, 64 per cent in Three Rivers and 61 per cent in the London Borough of Sutton during 2016/17.
Assuming an average rate of 25 per cent affordable housing if all the 30,575 new homes had been permitted under the normal planning route, the LGA estimates that the office-to-residential PD right has led to the potential loss of 7,644 affordable homes over the past two years.
Councils have also warned that the PD right is depleting office space needed by businesses and start-ups, the LGA adds.
Martin Tett, the LGA’s housing spokesman, said: "It is vital that councils and local communities have a voice in the planning process.
"At present, permitted development rules allow developers to bypass local influence and convert offices to flats, and to do so without providing affordable housing and local services and infrastructure such as roads and schools.
"Permitted development is detrimental to the ability of local communities to shape the area they live in."
A spokesman for the MHCLG said: "We are determined to build the homes our country needs and permitted development rights play an important role in helping us deliver more properties.
"We need a mix of dwelling types to meet different housing needs and over 17,500 additional properties were created by converting offices in the year to March 2017."
The MHCLG also pointed out that local authorities can remove PD rights through article 4 directions where they feel this is necessary .
The full research can be found here.