The push comes as a new report by the Alcohol Health Alliance found that some booze can be purchased for as little as 16p per unit.
It analysed 480 products to find the cheapest drink on sale across the UK.
Marolin Watson, from Christian drug and alcohol education charity HOPE UK, told Premier's News Hour there is an obvious solution to stop people binge drinking.
She said: "I think it's logical to assume that if alcohol prices go up, then people won't be able to afford to buy as much of it."
The study found almost seven-and-a-half litres of strong white cider can be bought for the same price as a cinema ticket.
Ms Watson said that education also has a key role to play in teaching children and young people their limits.
"Education has been surprisingly effective because on the whole children and young people are drinking less - but unfortunately the ones that do drink are drinking too much, some of them apparently consuming 15 unites per week - which is more than an adult should be drinking," she said.
She told Premier two solutions to the problem: "Increasing the unit price to at least 50p per unit," and "increasing tax" on alcohol.
Prices around the UK:
London cheapest Cider costs 16p per unit
North East beer costs 23p per unit
Scotland wine costs 32p per unit
At present, the Scottish government is looking at introducing a minimum alcohol price, but it has been held up in the courts.
A Home Office spokesperson said: "The harms associated with excessive alcohol remain too high - and current legislation prevents the sale of alcohol below the cost of duty plus VAT.
"Minimum unit pricing will remain under review while we monitor legal developments and the implementation of this policy in Scotland. The Government awaits the outcome of the case in the Scottish courts and we will continue to monitor developments."
Each year there are almost 23,000 deaths and more than one million hospital admissions related to alcohol in England alone.
Listen to Premier's Hannah Tooley speak to Marolin Watson here:
