Sterling dropped by two cents to a three-week low against the US dollar.
It was also down against the euro and hit a two-year low against the yen after London mayor Boris Johnson and a number of Cabinet ministers said they wanted to leave.
A weaker pound makes holidays more expensive for UK tourists but helps British exporters because it makes their goods cheaper in foreign markets.
The fall in the pound came after an EU reform deal reached by Prime Minister David Cameron ahead of an in-out referendum on June 23 that failed to satisfy his eurosceptic critics.
The text of the letter is understood to have been agreed with Downing Street.
Meanwhile a snap poll for the Institute of Directors revealed that six in ten business leaders plan to vote to remain in the EU following the agreement reached by Mr Cameron in Brussels on Friday.
Company directors believed the Prime Minister had secured a “reasonable deal” – with measures to reduce red tape, confirm that Britain would not be pulled into an “ever closer union” and protect the UK’s financial services industry – the IoD said.
IoD director general Simon Walker said business leaders had concerns about the way the EU operates but this was balanced against the ability to trade easily across the single market.
He added a worrying finding of the poll was that four in ten firms had not discussed the referendum in the boardroom.
Mr Simon Walker said: “Now that a date has been set, all firms should consider what the potential outcomes would mean for them.
“Amidst all the rhetoric and campaigning, it is vital that people appreciate the consequences for jobs, prices and economic growth.
“They need to hear what companies think.
“Business leaders will take different positions, but they should not be afraid to stand up.
“This referendum is a momentous political choice.
“Let us make sure it is a well-informed one.” By Agencies.
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