The energy watchdog, which is reviewing its merger policy under suspension, believes that dual fuel provider mergers can be beneficial for people seeking better deals.
But it also states they can be harmful to consumers, as they can reduce the regulator's ability to monitor them properly and work towards improving them.
According to Ofgem: "Customers should automatically receive a share of the efficiencies and other benefits that arise from mergers - all benefits should not be kept by shareholders."
The watchdog wants legislative action to make companies consider the impact upon its influence when carrying out mergers.
Ofgem's remit includes working to protect vulnerable people including the poor and elderly, as well as keeping gas and electricity suppliers efficient and as environmentally friendly as possible.
It also encourages competition within the sector for consumer benefit, such as cheap gas and electricity bills.
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