Tom Green and his wife, Keira, bought a flat in Solihull, near Birmingham, in February 2008 as the property market reached its peak. "We took on a 125% mortgage from Northern Rock – at that time it was sold as 'your property will increase in value, so it's no problem'," he says. However, just a couple of months later the market collapsed. "It's a big flat and there were just the two of us, so we decided to stay put and wait it out. We thought after a couple of years things would pick up," he says.

Instead, five years on, Tom Green thinks it is still worth less than the £122,500 they paid. They have watched as the neighbourhood has become less desirable and nearby properties have hung around on the market for years. "There are no first-time buyers left – they've all vanished, certainly at the level we want to sell at."

The couple are among a large number of would-be second movers trapped by negative equity and a scarcity of first-time buyers whose plight is highlighted in two new pieces of research.

Yesterday, Lloyds TSB's third annual Second Steppers report said that 61% of those who wanted to move up the property ladder in 2012 were unable to do so, while research published tomorrow by website Rightmove, will show that 40% of people hoping to buy their second property this year are living in homes their families have outgrown.

One in 10 told Rightmove they were trying to trade up despite living in a home worth less than they paid for it.

Of the 500 people interviewed by Lloyds TSB, 25% were in negative equity, while the same number reported a lack of offers on their home. Around a fifth thought it was harder to move up the housing ladder than it had been to get on it in the first place.

The lack of new buyers is underlined by Rightmove's research, which found that in six out of 10 regions of the UK the proportion of people saying they hoped to buy for the first time in 2013 was below 20%, less than half of the 40% associated with a healthy housing market.

Of the 4,000 would-be second movers who responded, 40% said their families had outgrown their homes, while 7% said the size of their property had made them put plans to start a family on hold.

Tom Peirson and his family are among those who are squeezed into a smaller space than they would like, but can't find the way to buy a bigger home.

Peirson, a firefighter, and his wife, Emma Jane, who runs a hairdressing salon, live with their two daughters in a two-bedroom home near Brighouse in Yorkshire. It is worth less than the £82,000 they paid in November 2005 and has been on the market since their youngest daughter was born four years ago.

He says: "We had an offer last year but they pulled out," he says. "We've just had another offer, but it's for less than we owe and, with all the other costs, we are not sure that we can afford to buy anywhere.

"If you are a young couple and can live at home you may be able to raise a deposit, but we are really struggling."

Government initiatives to kickstart the housing market have predominantly focussed on new-build property, to help the construction industry. But there are hints that the Budget could include measures to extend the NewBuy scheme, which allows buyers to take 95% mortgages on new homes (with some of the loan guaranteed by the government and developers) to existing properties – a move that could free up some of those trying to sell.

Rightmove says although second-time buyers made up 29% of those looking to move, their needs were not often considered. "Second-steppers are the ugly duckling of the housing market," says the website's director, Miles Shipside.

"Overlooked for government incentives, struggling to protect their equity if they bought near the peak, and now crammed into a home that is too small." He added: "It appears many second-steppers have had to shelve their family planning and home-moving ambitions since the onset of the credit-crunch over five years ago."

Psychiatrist Clare Gabriel (not her real name) lives in a two-bedroom flat in Glasgow with her husband and two children and runs a business from there. It cost £155,000 in 2005 and was recently valued at £120,000. "We have tried trading in with developers but they won't touch our flat," she says. The couple are trying to get their lender's permission to rent out their home so they can use Scotland's Mi new home scheme to buy somewhere bigger. "It is difficult because we want to live where there are decent schools and that means prices start at £265,000 ... Even if we did succeed we'd be taking a risk having two mortgages."

Back in Solihull, the Greens have family reasons for moving, as well as financial ones. They had a child in November, and rather than live in a second-floor flat with no lift, they moved in with Tom's parents. "If we sold now we would lose £10,000-£15,000 and we would need to find another £5,000 in fees – the last five years would have been a waste of time and money," he says.

Fortunately, the property was easy to let and since the start of the year they have had a tenant. "We realise we are lucky to be able to live with my parents while we save money and in 12 months we will be in a much better position."