European Union negotiators said on Friday an agreement with Britain was "very close" and European Commission President Jean-Claude Juncker said on Saturday a deal would be reached in November, if not this month.
That had helped push the pound up above $1.31, but investors booked profits at the start of this week, with some still cautious about whether a Brexit agreement was likely.
Analysts at Commerzbank said a deal remained a long way away, with both sides yet to agree on customs arrangements for the Irish border and Prime Minister Theresa May allegedly trying to gain support among opposition Labour party lawmakers to get a deal voted through parliament.
"To sum it up: Anyone who thought that an end of the Brexit drama is in sight will have to think again," said analyst Thu Lan Nguyen.
The pound dropped half a percent to as low as $1.3054 against the dollar, with a broader sell-off across markets and a rush into the safety of the US currency also sending sterling lower.
Versus the euro, the British currency weakened 0.1 percent to 87.955, slightly below 3 1/2-month highs touched at the end of last week.
Concerns about a row between Brussels and Rome over Italy's proposed budget deficit targets have added to the euro's woes in recent sessions.
Many strategists remain optimistic for sterling should the UK make more progress towards a Brexit deal.
"Overall, recent developments are encouraging as they help to dampen the risk of a more disorderly no-deal Brexit outcome. A Brexit breakthrough in the coming weeks would open up further upside potential for the pound heading into year end," MUFG analysts said in a note sent to clients.