Kemi Badenoch has challenged Andy Burnham to rule out fresh tax rises or increased borrowing to pay for his social care plans.In a letter to the Prime Minister, the Tory leader has warned against leaving it to 'the next generation to pay' for reforms.Mr Burnham is expected to make a major speech this week to set out his plans for overhauling the country's social care system, for which he is seeking cross-party support.He used a BBC interview this weekend to caution the NHS will 'collapse' unless action is taken - although he refused to put a timeline on when he would introduce changes.Reform of the social care system is unfinished business for Mr Burnham, who set out plans for change while he was health secretary in Gordon Brown's government.But his 2010 plans to overhaul social care for the elderly - with the creation of a 'national care service' for England - brought claims Labour would levy a 'death tax' to pay for it.In her letter to the PM, Mrs Badenoch reiterated her opposition to penalising those who have made provision for their care in later life.Unlike NHS care, social care is currently not free at the point of use, and high costs sometimes mean people are forced to sell their homes to pay for what they need. People with savings worth more than £23,250 are not entitled to help with the cost of care from their local council.Kemi Badenoch has challenged Andy Burnham to rule out fresh tax rises or increased borrowing to pay for his social care plans. In a letter to the Prime Minister, the Tory leader has warned against leaving it to 'the next generation to pay' for reformsMrs Badenoch wrote: 'Adult care spending alone is already £35billion a year and is only set to rise given our ageing society.'The Conservatives are happy to work with you and other parties on reforming social care. But we will only support a solution that abides by two core principles.'First, any solution to the issues around social care must also be fair to those who have made provisions and saved up over the course of their lives.'Second, the money must be found by reducing current spending. You must rule out any tax rises, or increased borrowing that will ultimately fall on the next generation to pay for.'The Tory leader noted how Government spending in 2028/29 under Labour is forecast to be £152billion higher than under the previous Conservative administration's plans, with taxes £105billion higher and borrowing £47billion higher.'With businesses closing or relocating, youth unemployment higher than in the eurozone, and the cost of living already causing real hardship for many people, the last thing Britain needs is further tax increases to pay for social care,' she added.Officials have already started drawing up proposals for a national care service, costing an estimated £18billion, although they are also working on cheaper proposals.Mr Burnham has repeatedly raised the idea of using a 10 per cent levy on all estates to fund it.Speaking to the BBC's Laura Kuenssberg, Mr Burnham said the NHS will never get back 'to good waiting time standards until we fix social care'.The PM said he would 'go as quickly as I can' on reforms, but declined to commit to creating a whole new system before the next general election in 2029.'I think there are major changes you can make before the next election,' he added.'The reason why I say I'll go as quickly as I can is because I believe broken social care is the biggest cause of corridor care in the NHS, it's the biggest cause of billions being spent on people unnecessarily going into hospital from care in their home or in a residential care home because sometimes the care workers supporting them have no choice but to ring 999.'Let me make this point because it's very personal to me. And then people have long stays in hospital, which never should have happened in the first place, and then they end up fit to go home but unable to be discharged because the social care isn't there. 'This costs the NHS billions of pounds… and we will never get the NHS back to good waiting time standards until we fix social care.'Mr Burnham also promised to put 'whatever political capital I have' into fixing the 'broken' social care system.'I would not want to leave office without having brought in substantial change,' he continued.'I can't put a timeline on it right here, right now. If we don't do it, the NHS will collapse under the weight of trying to care for people who've not really needed to end up in the NHS system.'Responding to the PM's comments, Liberal Democrat leader Ed Davey, said: 'I know for a fact this morning that carers I know will feel a sense of hope that politicians may finally do something serious to fix care in our country.'I am ready to roll up my sleeves and do whatever I can to find a real and lasting consensus on social care.'Family carers must be at the heart of any new system, everyone must get the care they need and no one should lose their home as a result.'