Its analysis found that prices will be out of reach for all people in need of affordable housing in 220 council areas (67%) and are out of reach for more than 90% of people in need of affordable housing in a further 80 (25%) council areas.
People in need of affordable housing are defined as those who would have to spend more than 30% of their household income to rent or buy a home.
For the average earner with a 5% deposit, a 20% discount would make it possible to borrow enough to buy a starter home in just 45% of all council areas in England.
First-time buyers will be able to buy 200,000 new starter homes over the next five years at a minimum discount of 20% to the market value. Discounted prices will be capped at £450,000 in London and £250,000 elsewhere.
The 20% discounts for new buyers would be funded by exempting developers from paying Section 106 contributions towards affordable rented housing and Community Infrastructure Levy contributions. In its own analysis, the Government has suggested that should 100,000 starter homes be built through the planning system, between 56,000 and 71,000 social and affordable rented homes would not be built.
Although house-builders will be able to build and sell starter homes below the price caps, councils are concerned that this could be difficult for developers to achieve without compromising on quality, particularly in areas with higher house prices.
The LGA is urging Lords to back amendments allowing councils to continue to ensure a mix of affordable homes based on local needs and to ensure that councils have the means to invest in the vital infrastructure home buyers and communities will rely on.
Discounts on starter homes should also be applied to them when they are resold to benefit future generations and help them also get on the housing ladder, it said.
Cllr Peter Box, LGA Housing spokesman, said:
"The shortage of houses in this country is a top concern for people who are finding that buying their first house is increasingly out of reach. Councils support measures to boost home ownership and starter homes are one of the ways this can be achieved.
"This new analysis shows that starter homes will be out of reach for the majority of people that are in need of an affordable home. Not everybody is ready to buy, and it is crucial that councils are still able to ensure there is a mix of homes that are affordable for those people that need them.
"In some places, such as the North-East and Midlands, the scheme will give people better chance to get on the housing ladder. However, a national scheme will not work for every area and fewer people will benefit from Starter Homes in areas where the housing crisis is most acute.
"Councils must have the flexibilities to shape the number, location and types of starter homes to ensure that they meet local need, and the powers to secure vital investment in associated roads, schools, health and other community services that people will rely on.
"The private sector has a key role to play in solving the housing shortage, but it cannot build the 230,000 needed each year alone. Councils need to be able to ensure genuine affordable homes continue to be built for rent and sale across the whole country for future generations and the millions of people stuck on waiting lists."
