The pound had already fallen against both the euro and the dollar on Monday on worries over Prime Minister Theresa May's future, after a newspaper report over the weekend that as many as 40 of her lawmakers would support a no-confidence motion against her.
It added to those falls on Tuesday after the inflation numbers, slipping to 89.53 pence per euro, down 0.6 percent on the day and the pound's weakest since Oct. 26.
"The market is reacting more to soft news and anything that could move sterling lower - on both the data side and on the politics side," said UBS Wealth Management currency strategist Geoffrey Yu.
Tuesday's numbers showed consumer price inflation held at an annual rate of 3.0 percent in October, below economists' average expectation in a Reuters poll for a 3.1 percent annual rise.
The BoE said this month, after it raised interest rates for the first time in a decade, that inflation would probably peak at 3.2 percent in October and then fall slowly.
Tuesday's figures, therefore, are likely to reinforce doubts among economists about the wisdom of the BoE's decision to raise rates at a time when the economy is sluggish, especially as the effect of last year's Brexit vote on import prices was already at its high point.
Sterling fell to as low as $1.3075 after the data, down from $1.3115 before its release and around 0.3 percent lower on the day.
Britain's internationally focused FTSE 100 stock index jumped to a session high after the data, while British government bond prices rose.
With the inflation data out of the way, the next focus point for sterling traders is the prime minister's European Union withdrawal bill, with lawmakers set to try to win concessions from the weakened leader.
"As Brexit woes continue to hinder a UK government that seems to be in self-combust mode of late, the weakening local currency has also started to reflect the lack of confidence in Theresa May's government, which won't help sterling rebound unless Brexit negotiations bear fruit," said Anthony Kurukgy, senior sales trader at Foenix Partners in London.