A radical demographic shift means that Britain's ethnic minority vote may determine the outcome of the 2015 election, according to research.

A study by the cross-party group Operation Black Vote (OBV) found the number of seats where black and Asian voters could decide the outcome had rocketed by 70% compared with the 2010 election.

The study suggests that in 168 marginal seats, the ethnic minority vote is bigger than the majority of the sitting MP. The seats extend beyond inner-city areas to include places such as Southampton, Oxford, Sherwood, Ipswich and Northampton.

The findings will be of particular concern to the Tories, who have acknowledged that they are struggling to capture the ethnic minority vote. The party secured only 16% of the minority vote at the last election, compared with 68% for Labour. Experts say the trend will continue and may change the dynamics of British politics.

Simon Woolley, of OBV, said: "The black vote has never been so powerful. This is great news for all those who thought we could never effect change … With this political leverage I'm sure many will want to demand greater race equality …This research is a political game-changer – above all, if ethnic minority communities and politicians respond positively to it, democracy wins."

The Liberal Democrat deputy leader, Simon Hughes, said the findings were "very significant" and added: "Unless all parties and candidates engage with and seek to win BME [black and minority ethnic] support, they could be in political difficulty locally and see their general election prospects significantly set back."

According to one new estimate, the change in Britain's ethnic makeup may already be enough to cost David Cameron the next election. The Conservatives' race deficit will cost them between 20 and 40 seats in 2015, according to calculations by Prof Anthony Heath, of Oxford University, who has studied ethnic demographic changes and their effects on elections.

In 2010, Labour polled its second worst result ever, but the party still thrashed the Tories in the ethnic minority vote, where its 68% to 16% win contrasted with the Tories' overall 36%-29% victory. Operation Black Vote estimates that the BME vote was bigger than the sitting MP's majority in the 2010 election in 99 seats, but those figures are based on the 2001 census, so probably underestimate the impact.

The Tories fell short of a majority by 20 seats. Heath, in estimates for a forthcoming book, says 10 of those were down to their race problem. "Minority voters can be won away from Labour, but only if you make active efforts, including addressing their concerns. There is little sign of long-term erosion from Labour," he said.

Tory insiders acknowledge that they have recently introduced eye-catching measures in areas with high immigrant populations – including adverts telling illegal immigrants to go home – as they try to hold on to white working-class and lower middle-class voters who are moving to Ukip. But these measures tend to play badly with ethnic minority voters.

Nadhim Zahawi, the Tory MP for Stratford-on-Avon, who has called for an amnesty for illegal immigrants, said the findings should lead to a redoubling of efforts to attract black and Asian voters. "These numbers are significant. The ethnic minority vote is going to be important. The party is in the midst of a debate and it is an issue which is now being taken seriously," he said.

Besides growing in numbers, minorities are moving out of inner cities into more marginal seats. This double whammy will increase their electoral importance in 2015 and is expected to feature even more prominently in future elections.

In 2001, the census showed Britain's ethnic minority population was 7%, and this had grown to 11% by the 2011 census. According to the OBV study, the ethnic minority vote will be crucial in swing seats from the Midlands to the south coast, across to East Anglia, and in the north-east.

The number of ethnic minority voters exceeds the sitting MP's majority in six of Birmingham's 10 seats, both seats in Blackpool, Brighton, Newport, Northampton, Norwich, Ipswich, Plymouth and Portsmouth, all three of Southampton's seats, and in Newcastle and battleground London seats.

Privately, leading Tory figures fear their chances of victory will be hampered unless they improve their insipid appeal to ethnic minority voters. Figures such as Lord Ashcroft, the former deputy chairman and treasurer, fear the party has a race problem, and he has commissioned polling that demonstrated this.

In the 2012 US election the defeat of the Republican candidate, Mitt Romney, was blamed in part on a failure to connect with a growing ethnic minority vote.

Labour's efforts to secure and increase its huge ethnic minority lead are being led by Sadiq Khan, the MP who ran Ed Milliband's leadership campaign.

Khan said: "The DNA of politics needs to change in the light of this research." He added: "This research shows how important the ethnic minority electorate is going to be in future general elections. Any party that seriously wants to win needs to take the ethnic minorities with them."

Labour cannot count on continuing to dominate the ethnic minority vote, warned Khan, who expects the Tories to try to compete harder. He pointed to the Bradford byelection, where Muslim voters turned their backs on Labour and cost the party the seat as they backed George Galloway's Respect party. "We can't take ethnic minority votes for granted," he said.

If the Conservatives fail to win an outright majority in 2015 it will mean their last such majority was almost a quarter of a century ago, under John Major in 1992. Heath said: "The Conservatives may need to adjust their appeal in the same way Labour created New Labour to deal with the decline in the working class [vote]."

In 2010 the Conservatives won 306 seats, 20 short of a majority, to Labour's 258, with the Lib Dems taking 57. For 2015, the Conservative strategy is to try to hold their 40 most marginal seats and gain 40 more to give them outright power.

Cameron has given Tory vice-chair Alok Sharma, MP for Reading West, the task of boosting the party's ethnic minority appeal. Sharma said: "The analysis … speaks for itself in highlighting seats with larger numbers of voters with an ethnic minority background and their potential electoral impact. But ultimately what matters to everyone who wants to work hard and get on in life, whatever their background, is fixing our economy."

• This article was amended on 15 August 2013 because Birmingham has 10 constituencies, not eight as the original said.