Jeremy Corbyn is being urged to tackle a £10bn black hole in provision for older people to help Labour build a coalition that can deliver a majority at the next election.

With the main parties neck and neck in the polls, senior figures on the left want Labour’s leader to commit to higher spending on the disabled elderly, which could narrow the Tories’ huge lead among older voters.

A new study by the Fabian Society, the leftwing thinktank affiliated to Labour, identifies a £10bn gap in provision for the disabled elderly. Half the shortfall comes from shortages in social care funding, which have left 1.2 million older people without enough help to carry out basic day-to-day activities such as washing, dressing and eating.

The research finds a £1.5bn gap in NHS rehabilitation services and £1.3bn in council-funded care home places and believes a “cautious” £1.2bn extra funding is needed to tackle problems caused by isolation and prevent accidents. It also reports a £900m shortfall in specialist housing. The extra money would bring the UK in line with other countries, it states. It warns this gap can only grow over the coming decades as the elderly population expands.

Labour has looser spending commitments than the Tories, but some fear it has done too little to win over older voters. A recent poll for the Social Market Foundation found only a quarter of those aged 65-74 would consider voting Labour at another election. The figure included the 25% that voted for the party in June last year, suggesting that Labour needs to change its offer to older voters.

Only Labour can convince the public that it will provide the support and dignity older people deserve Andrew Harrop

Britain spends about £25bn on support for the disabled elderly, but the Fabians believe the bill to provide just this same level of support – which it deems grossly inadequate – will balloon to £40bn by 2030. Spending will need to rise even further, to roughly £60bn by 2030, to meet existing unmet need and to respond to rising demand and costs.

The research will be presented to a summit of Labour politicians, experts and charity leaders on Monday.

Andrew Harrop, general secretary of the Fabian Society, said: “As a country, we need to spend billions more each year to support frail pensioners both because the number of people who need care is rising so fast and because the help on offer today is so inadequate.

“Labour can lead on this agenda because it is the only party with the courage to say that big spending increases will be essential each and every year. The party needs to explain where the money is coming from, but with a clear new offer it can convince the public that only Labour will provide the support and dignity older people deserve.

“After the 2017 election the Labour party knows it needs to regain the trust of older voters, and making a credible promise on support and care will help it do that. Promising to spend more on help for frail pensioners is true to the party’s values and it is what people want and expect.”