The brewer and pub operator has also argued a lower price would not have enough of an impact on public health and has urged the Government to commit more cash to tackle the UK drinking culture, increase alcohol education in schools and introduce extra restrictions or measures for the off-trade.
Greene King made the suggestions in written evidence it has submitted to the health select committee inquiry into the Government's Alcohol Strategy published in March which called for a minimum price for alcohol of 40p per unit.
However since its publication the Scottish Health Secretary Nicola Sturgeon saw her plans for a 10p higher minimum price north of the border passed by the Parliament in Holyrood.
Now the Suffolk-based company has urged the Westminster Government to react in order to avoid confusion.
"Different levels would be potentially divisive, confusing to consumers and would potentially cause domestic 'booze cruises' across UK national borders," Greene King said.
The company has been vocal about its support for the policy of minimum pricing in the past and has now argued differing levels could lead to problems already faced by different US states. "Government would also have to police illegal cross-border activity," the brewer and pubco added.
Although there has largely been agreement on the minimum pricing policy within the hospitality industry, several leading figures have questioned the likely effectiveness of the plans.
In a short audio podcast earlier this year Tim Martin, chairman of J D Wetherspoon argued drinkers should be encouraged to head to their local boozer if the Government wanted to tackle binge drinking.
However last month Brigid Simmonds, chief executive of the British Beer and Pub Association (BBPA), suggested the Government include a 'sunset clause' in any minimum pricing bill to allow it to be reversed if it proved not to be as useful as hoped.
Greene King said it continued to back minimum pricing in principle but argued in its written evidence that a code was needed for everyone involved in the policy to effectively tackle binge drinking.
The company also called for fewer restrictions on pubs and restaurants but more rules to apply to the off-trade which might include: "Restrictions on the availability of alcohol in unsupervised environments and specific restrictions on promotions, alcohol displays, time of sale and better health education."