The pound is taking a hit on 'Brexit' fears
It adds to uncertainty over the country's future in the bloc. One in three voters in the UK consider Johnson's position as "important" in deciding which way to vote, according to a recent Evening Standard poll.
Here's how key GBP (Great British Pound) trades look at 7.05 a.m GMT (2.05 a.m. ET), as per Investing.com:
The deal sets the stage for campaigning to start in earnest over a so-called "Brexit" ahead of a referendum on June 23.
Cameron is calling for Britain to stay after the deal, but the "In" camp took a blow when London Mayor Boris Johnson on Sunday said he would support leaving the 28-member bloc.
"Even if an exit isn't likely, uncertainty and concerns about it will continue and weigh on sterling," Kengo Suzuki, chief currency strategist at Mizuho Securities, told Bloomberg News.
"On the economic front, there isn't much to undermine the currency, but the uncertainty over a potential exit will cap sterling, keeping it in a $1.40 to $1.50 range."
The diving sterling comes amid reports that Brexit fears are also making it tougher for UK companies and banks to issue bonds. The Financial Times reports that foreign investors are raising the possibility of a Brexit and its effects as a key concern with British companies looking to issue debt.
The City of London is largely pro-Europe, with the Independent reporting that top management from more than a third of FTSE 100 companies are set to sign a letter issued Tuesday calling for Britain to remain in Europe.
In other trading, the dollar firmed to 112.87 yen from 112.62 yen, although it was still lower than the levels above 113 yen seen most of last week.
Analysts said the yen -- seen as a safe haven in times of turmoil -- may rise again on lingering concerns about Britain's future EU membership and unsteady oil prices.
Markets are also eyeing Japanese inflation and revised US GDP data due this week, and a meeting of ministers from the Group of 20 set to start Friday in Shanghai.