The BMA also warned that plans to introduce personal care budgets set out in the white paper risked increasing variation in services people receive across England.
BMA chairman Dr Mark Porter said: 'How to deal with our aging population is a pressing problem for society, and the NHS in particular, and it is only going to become more acute, so it is very disappointing that we are still no clearer as to how social care is going to be funded.
'While ministers shy away from this, the costs of caring are being increasingly borne by the health service and until a solution is found the NHS and social care system will continue to struggle to cope.'
Health secretary Andrew Lansley said the government's plans would bring 'the most comprehensive overhaul of social care since 1948'.
Mr Lansley said that the government backed recommendations in last year's Dilnot review, including 'financial protection through capped costs and an extended means-test'.
But he added: 'However, while this is the right thing to do and it is our intention to base a new funding model on the principles, if a way to pay for it can be found, any proposal which includes extra public spending needs to be considered alongside other spending priorities. The right place to do this is at the next spending review.'
NHS Confederation chief executive Mike Farrar said: 'We urgently need a firm, cohesive plan about how funding for social care will work in the future. We need an open and honest debate about what the state can afford to provide and what individuals will have to pay for.
'It is absolutely essential that the government makes clear the financial implications a cap on care costs could have for people who choose to opt in to any future funding programme.
'We need to take action on this issue now. The country cannot afford to pick up the pieces of a broken social care system. The longer we wait the worse the problem will grow.'