Inflation dropped to 2.6% in June from 2.9% the month before, whereas economists had expected no change.
Sterling had been trading above $1.31 at one point before the inflation figures were released.
However, the inflation data sent the pound down to $1.3038 at the end of London business.
The pound also fell 1% against the euro to 1.1251 euros.
"Today's slowdown in price growth should squash any speculation of a rate hike for the time being," said Neil Wilson, senior market analyst at ETX Capital.
"An August rate hike now looks highly unlikely, but we should remember that the Bank has only limited tolerance for continued above-target inflation and may yet seek to push rates back up to 0.5% this year, if conditions in the wider economy improve whilst inflation remains above 2%."
The fall in the pound initially lifted the FTSE 100 share index. The FTSE 100 often moves inversely to sterling, as a weaker pound boosts the value of overseas earnings of the multinational companies in the index.
Having been more than 40 points lower at one point in the morning, the FTSE 100 closed down 13.91 at 7,390.22.
Royal Mail shares rose 3% after the company reported a 1% rise in revenues in the three months to 25 June, helped by its Europe-wide parcels business GLS.
In the UK, the volume of letter deliveries fell again, although general election political mailings helped to slow the decline.
The pound fell against key currencies after an unexpected slip in inflation - seen as easing pressure on the Bank of England to lift interest rates.