They are under pressure from voters to limit building development but planning guidelines make it hard for them do so.
Unless they have a five-year supply of housing land, developments that are refused can go through on appeal.
To fight an appeal "will cost a lot of money" and councils are "strapped for cash", said consultant David Shaw.
The East region is one of the fastest growing parts of England and the government is keen to increase the rate of house building.
Mr Shaw, a Peterborough based town planning consultant, said: "Councils are very strapped for cash these days.
"If they are going to have to fight an appeal they know that will cost them a lot of money and they're frightened of that. So they're making decisions that they are really reluctant to make."
Local authorities are obliged to have a five-year housing land supply as part of the National Planning Policy Framework published in March 2012 by the Department for Communities and Local Government.
The aim of the framework is to make the planning system less complex and more accessible, the department said.
If a local authority does not have a clearly stated five-year housing land supply planning policies for new homes will be considered out of date.
This means a government inspector can override a local decision on appeal using this one provision.
Source:National Planning Policy Framework
North Hertfordshire District Council is in a high-growth area under pressure to accept more new homes than local people want. It recently approved plans for 150 homes at Ivy Farm, Royston.
David Levett, planning portfolio holder for the council, said: "It wasn't the ideal site but on balance we felt that if we refused it and it went to appeal, it would almost certainly be approved by the inspectors.
"We haven't got a five-year land supply and... that's why we approved it."
Mr Levett denied that the costs of an appeal were a factor at Royston.
Â£242,000
was the average (mix adjusted) price of a property in the UK in 2013
21,050 homes were started by private enterprise, housing associations and local authorities in the East
19,040 homes were completed
27.8m residential properties make up the UK housing market
Other councils claiming to have a five-year land supply have still found their decisions overturned on appeal.
South Cambridgeshire District Council refused plans for 150 new homes at Waterbeach. But the planning inspector later approved them, saying the council could not "demonstrate" a five-year land supply.
Robert Turner, the council's planning portfolio holder, said: "We were very disappointed to see a major decision like that overturned.
"Applications are coming to us and even if we don't like them, and refuse them, the government has obviously got a bigger picture and can grant them on appeal."
In Clenchwarton, near King's Lynn, an application for 40 homes was turned down by the Borough Council of King's Lynn and West Norfolk because the site was outside the village development boundary and prone to flooding.
But it was allowed on appeal, again, because the inspector said the council could not demonstrate a five-year land supply.
The council, which says it has a seven-year land supply, is taking the appeal decision to judicial review.
Figures from the Home Builders Federation (HBF) indicate the government estimates about 27,000 homes a year are needed in the east region.
"We estimate that local authorities are planning for around 3,000 fewer homes than this per year," said spokesman Steve Turner.
"However, the number of new homes actually being started is much lower, and we estimate that well under 20,000 new homes were started last year.
"Each year there is an undersupply and this only exacerbates the shortage of homes in the region further."
In Essex, Tendring District Council consulted voters before drawing up a draft housing plan recommending 6,000 new homes.
But a government planning inspector said this was not enough - so 12,000 new homes has now been proposed, with a new consultation soon to get under way.
Council leader Mick Page said: "The government is saying housing numbers are down to us as a local authority but really they're not.
"It's government policies which are given to the inspectors who come down here and dictate what they want."
The importance for councils to have a local plan has been stressed by housing minister Brandon Lewis as not enough homes are being built.
He said the Localism Act of 2011 had strengthened the role of councils and abolishing regional housing targets gave people more control over where homes should be built.
"Since the National Planning Policy Framework was introduced, the number of appeals (against rejected schemes) received has fallen, as has the number allowed," he said.
"The quality of local decisions also remains high - 99% of decisions are made locally with only about 1% of planning applications overturned on appeal.
"Our reforms are supporting badly needed new homes within a locally-led planning system."
Councils in the east of England feel forced to back plans for homes because they are "frightened" to reject them, a BBC investigation has found.