The communities and local government committee said the eight biggest firms built more than half of all new homes.
MPs said the government should do more for smaller builders who do not have the scale to bid for big projects.
But the Home Builders Federation, which represents large and small businesses, said only big firms could spread the risks large-scale projects pose.
The committee also said local authorities should prepare land for home building.
That would include providing the infrastructure needed, such as roads and public transport.
"The housing market is broken, we are simply not building enough homes," said Clive Betts MP, chair of the committee.
"Smaller builders are in decline and the sector is over-reliant on an alarmingly small number of high-volume developers, driven by commercial self-interest and with little incentive to build any quicker.
"If we are to build the homes that the country so desperately needs, for sale and for rent, then this dominance must end."
Government promises more affordable homes
Labour promises to build one million new homes
The committee found that smaller builders struggled to obtained land for development, as local authorities focused on large sites which only big companies could afford to take on.
The Homebuilders Federation said: "We fully support the committee's call for measures to assist smaller builders, encourage new entrants and scale up specialist housing sectors, such as the retirement housing market.
"The vast majority of the big increases in housing supply in recent years have come from the larger, mainstream builders - but we need more builders of all sizes and specialisms if we are to tackle our acute housing shortage."
In February the government promised to build more affordable houses and help people buy and rent, after admitting the current market was broken.
The housing strategy for England included giving councils powers to pressure developers into starting building on land they own.
Ministers also pledged to make renting more "family-friendly" with longer tenancies offered.
However, Labour called the measures announced "feeble beyond belief".

Mousinho, 31, has captained the Brewers in all three Football League divisions, but had not played in the second tier before last season.
"The Championship was a bit of an unknown for me," he told Burton's official website.
"Now I feel in a better place with that season under my belt."
Mousinho made 32 appearances in the Championship in 2016-17, starting in Burton's victories over Sheffield Wednesday, Norwich, Huddersfield and Leeds, all sides who finished in the top eight.
And while he admits the Brewers will no longer carry the element of surprise, Mousinho says the team, who were playing non-league football less than a decade ago, will be stronger following their maiden campaign at Championship level.
"Maybe a few underestimated us last season and I don't think that will happen again," he added.
"It will be a completely different challenge but we have more experience, we know what it takes, what the level is all about and as last season went on we got better and better.
"Next season I think we will be set up well but there will be new challenges and we will relish that."

The 49-year-old Portuguese replaces Stuart Gray, who parted company with the Championship side on 11 June after 18 months in charge at Hillsborough.
Carvalhal has managed extensively in Portugal and also had a spell in charge of Turkish club Besiktas.
"I firmly believe that this appointment will take our team and our club to the next level," said Owls chairman Dejphon Chansiri, who took over in March.
BBC Radio Sheffield says Wednesday want Swindon Town boss Mark Cooper to assist Carvalhal, who will be formally unveiled on Thursday and takes over a side that finished 13th in the second tier last season.
Wednesday have not been in the top flight since being relegated in 1999-2000 and Chansiri has targeted promotion in the next two seasons.
"It is important for our supporters that they watch their team play attractive, aggressive and entertaining football," he added on the club's website.
"Carlos buys in completely to this philosophy and I am confident that his experience, knowledge and ability will herald the start of a successful new era for Sheffield Wednesday."
Cooper, 46, has been in charge of Swindon for the last two seasons and led them to the League One play-off final last season.
Joao Mario, Joao Cunha and Bruno Lage have already been named among Carvalhal's backroom staff.
MPs have called for an end to the dominance of big home-building firms to fix the "broken" housing market.
[NEXT_CONCEPT]
Burton Albion skipper John Mousinho says he is relishing a second season in the Championship after signing a new one-year contract.
[NEXT_CONCEPT]
Sheffield Wednesday have named Carlos Carvalhal as the club's new head coach.