Mr Lansley wants doctors to have more say and to set up better deals with manufacturers to reduce prices.
But Mr Appleby told BBC Radio 4's Today programme: "The £200m they say will be needed to fund extra cancer drugs essentially has to come out of the current budget. That means stopping something else for other people.
"It's a sleight of hand in the sense that the money is not there to be saved."
Mr Appleby said there was often disagreement between those cancer specialists who wanted greater access to drugs and others who believed medication which was yet to be licensed or approved by Nice may not be cost-effective.
He also said Nice had approved the majority of cancer drugs it examined.
The King's Fund later said Mr Appleby did not mean to imply there was anything dishonest about the Conservatives' proposals.
It said in a statement: "If the phrase 'sleight of hand' used when commenting earlier today suggested this, he would wish to withdraw it."
Nice has said it is wrong to advocate the use of treatments where the additional benefit of a drug is uncertain.
This comes on top of our commitment to provide real increases to the health service budget
Shadow chancellor George Osborne
GPs' representative Dr David Jenner said it was a good idea for specialists to decide which drugs the NHS should fund for rarer forms of cancer.
But the doctor, a policy adviser for the NHS Alliance which represents primary care trusts, said cancer spending had to be justified against a backdrop of tightened budgets.
"Expenditure on cancer drugs can be very high-cost, low-volume; [you are] spending a lot, sometimes to give people a few months' extra life," he told the BBC.
"When it's not a bottomless pit you've got to see how many other procedures you could buy for the same amount of money, like how many hip replacements you could fund, how many educational programmes for diabetes, for example."
Investing in equipment to help GPs diagnose cancer earlier could save more lives, he added.
Mr Lansley said: "If people have a cancer [and] maybe some of the existing treatments haven't worked and their doctor, their specialist, says a particular new cancer drug should be provided for them, we believe that should happen."
Labour's Andy Burnham and Shadow Chancellor George Osborne talk about funding for cancer drugs
He said primary care trusts were budgeting for making increased NI payments.
"It is a saving compared to where they expect to be," he said.
Mr Lansley also denied a higher value was being placed on cancer patients than, for example, people with Alzheimer's.
He added that the party was confident the measure would not cost more than £200m.
Shadow chancellor George Osborne said the pledge amounted to a "clear difference of priorities" from Labour and that the savings were not being "magicked from nowhere".
"This comes on top of our commitment to provide real increases to the health service budget... and our commitment to make sure that there isn't wasteful government spending in the NHS," he added.
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