The warning came as the government announced its own scheme to raise public awareness of the cost of drugs.
This will mean that patients see the true cost of their prescriptions together with the words "funded by the UK taxpayer," according to health secretary Jeremy Hunt.
The plan was launched as the NHS England clinical director overseeing specialised services warned the drug costs used for these treatments are predicted to rise at 11% a year.
Speaking to a conference, the clinical director James Palmer, a neurosurgeon, said it was unlikely the NHS would be able to afford these increasing costs in specialised services - as it is set to prioritise care out of hospital.
He said the increased cost would come in spite of arrangements to reduce the cost of new medicines.
Reported by the Health Service Journal, he said: “We can’t afford everything, and there will be drugs and treatments we can’t afford.”
He added: “I think the chances of specialised services having a significant growth allocation of money, to deal with the 11 per cent growth at least in drugs, is not going to happen.”
Mr Palmer explained: “The reality of my work as a neurosurgeon is that the problem isn’t access to drugs, it’s access to beds, because the system is getting really broken.”
The pressure will come from the clinical commissioning groups that have taken responsibility for primary care budgets, according to the Health Service Journal.
There are 63 of these CCGs and 21 said they planned to put cash into helping practices form federations.
Another 15 said most or all of their practices were already in federations - while 24 said they did not have plans.
Federations have been seen as a way of enabling GPs to manage more services. But some CCGs said they were concerned it would create conflicts of interest.
In East Leicestershire and Rutland, practices are to be paid £2.50 a patient over two years to cover the cost of creating federations.
But a spokesman for Vale of York CCG told the journal: “Because of the commercial sensitivities around awarding contracts, the CCG does not feel that it should preferentially incentivise or facilitate the formation of GP federations, which could then bid, against other potential providers, for CCG contracts."
According to Dr Julian Archer, from Plymouth University Peninsula Medical School, research into health care education suffers from a lack of funding.
And most research that is undertaken is performed by "enthusiastic amateurs," he says.
Writing in The BMJ, he has argued that future training of doctors is being "left to chance."
Improved training and education could help prevent medical errors, he says.
He quotes a recent survey in Wales showing that out of 45 health education researchers, just four had attracted grants worth £100,000 or more over four years. And only 24 had received any funding at all.
He said: "In our editorial we liken the lack of health care education research funding to bringing in constant improvements to the look and performance of a car, only to undermine those improvements by investing only in the cheapest oil.
"At a time when errors in the clinical workplace hit the headlines with a worrying frequency, and the levels of compensation are so phenomenal that there is a serious call to cap pay outs in the UK, now is the time for funding bodies to support us - the 'Cinderella' of health research - to provide the evidence base required to train health care professionals effectively."
He added: "To us and to many in the health professions the advantages are obvious: an optimally trained clinical workforce; a contribution to avoiding preventable medical errors; efficiently and effectively run health services; and ultimately improved care and clinical outcomes for patients."
The findings come from a randomised study involving more than 1,000 men and post-menopausal women, conducted in California, USA.
It has been claimed previously that low cholesterol levels may increase aggression.
But the researchers found that, in men, any effect of this kind was counteracted by the effect of statins in reducing levels of the hormone testosterone.
In women there was a significant effect for women over the age of 45.
But this may be caused by the effect of the drugs on sleep, the researchers say. They found a strong link between sleep problems and increased aggression.
The findings have been reported in the journal PloS One.
Researcher Professor Beatrice Golomb, of the University of California, San Diego, said: "Either men or women can experience increased aggression on statins, but in men the typical effect is reduction."
Statin Effects on Aggression: Results from the UCSD Statin Study, a Randomized Control Trial PloS One 1 July 2015 [abstract]