Thames Water, which supplies five million people in London, has applied for a drought order.
The order would affect London and small parts of Kent and Surrey, but leave three million other customers in the Thames Valley unaffected.
Chief executive Jeremy Pelczer said a hosepipe ban had been in place for two months but dry conditions meant further restrictions might be needed.
He said the water supply situation was "serious" despite recent rain.
The application will be subject to an independent inquiry before the government decides whether to approve it.
The process could take up to eight weeks.
Small business impact
Thames Water has not ruled out applying restrictions to other areas later in the year.
"Applying for a drought order is also an essential step in the process of getting approval from the Environment Agency to take more water from the rivers than we are normally allowed," said Mr Pelczer.
"This extra water would help us to maintain reservoir levels and make further restrictions less likely."
Last July, Thames Water was criticised by regulator Ofwat for losing 915m litres of water a day.
"No water company likes restricting its customers' use of water," said Mr Pelczer.
"We are particularly mindful of the impact a drought order would have on many smaller businesses. This is why we would only implement any powers granted under a drought order as and when necessary.
"This all depends on how much rain we get in the coming weeks, but we must ensure we can continue to provide water for essential purposes, however dry the summer might be."
Two dry summers have caused low river and groundwater levels across Thames' Water's catchment area.
Consumer Council for Water spokesman Andrew Marsh said: "I am very concerned because Thames Water have a poor record on containing leakages from their network and so they will find it harder than other companies to take customers with them in conserving water resources.
"Our particular concern is about those businesses which are water-dependent because their livelihoods could be affected by a drought order."
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