"The situation is a disaster and we're trying to locate survivors and help people but everything is flooded and people can not leave their homes", said Antonia Bauza, a senior official at San Llorenc mayor's office.
The Britons and two local residents died in the town of Sant Llorenc des Cardassar, the town's deputy mayor, Antonia Bauza, told Cadena SER radio.
A Foreign Office spokesman said: "We are supporting the family of two British people following their deaths in Spain, and will do all we can to assist them at this deeply hard time".
At least another 20 people were still missing after the downpours, local media reported, though emergency services would not confirm that figure.
Torrential rainstorms deluged the town of Sant Lorrenc, about 65km east of the capital Palma, yesterday evening.
People walk along the damaged waterfront after a storm on the island of Mallorca, Spain, on October 10, 2018.
At least three towns closed schools and hundreds of people were given shelter in sport facilities.
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Two men were found dead around midday on Wednesday, one in the northeastern town of Arta and another at S'illot further south on the coast.
Forecasters said that eight inches of rain fell in four hours.
100 rescue workers and 80 soldiers have already been sent to the most affected areas of the island.
At least 220 millimetres of rain are believed to have fallen in the region, flooding homes, roads and fields.
Sanchez will be flying to the area later Wednesday, his office said.
Lawmakers held a minute's silence before the weekly prime minister's question time in parliament on Wednesday morning.