Thames Reach chief executive Jeremy Swain said the price of a 50cl can should be pegged at a minimum of £2.25.
In a letter to Chancellor George Osborne, Swain said: "We would also back any plans introduced by your colleagues in government to give lcoal councils the powers to clamp down on these drinks."
Swain branded superstrength beer and cider as "undoubtedly the biggest killer of homeless people in the UK".
He added: "In an age of corporate responsibility, it is irresponsible that drinks companies are producing half-litre cans of 9% superstength lager which contain 4.5 units of alcohol."
He said white ciders were "cheaper than lemonade".