The report in the Evening Standard pushed sterling up against the dollar and euro, dragging the exporter-heavy FTSE 100 off earlier highs and down 0.4 percent. But the currency fell back after a spokeswoman for British Prime Minister Theresa May ruled out any delay.
Companies that earn mainly U.S. dollars are hit by a stronger pound and were the among the biggest drags on the index. AstraZeneca fell 3.6 percent, while HSBC and GlaxoSmithKline also fell.
But weakness in oil majors BP and Shell on lower crude prices made the sector the biggest drag on the FTSE 100.
The Evening Standard cited unnamed cabinet ministers as saying Brexit looks increasingly likely to be delayed beyond March 29 because of the backlog of legislation that needs to be passed.
Stocks had been boosted earlier by reassurance from U.S. Federal Reserve Chairman Jerome Powell on the pace of further increases to interest rates, with progress in U.S.-China trade talks also providing support.
Mid-caps, which make half of their income at home, rose 0.6 percent to their highest in more than a month.
David Madden, CMC Markets analyst, said any Brexit delay might provide a short-term bounce for the pound but emphasised that the outlook remains highly uncertain.
"All the various options, be it Theresa May’s plan, a second referendum, or leaving the EU without a deal – they all seem to be almost equally unpopular,” he said.
British homebuilders <.FTNMX3720> sensitive to Brexit news, extended early gains to trade up 2.1 percent as the sector index <.FTNMX3720> registered its biggest weekly gain in nearly three years, helped by Bank of America Merrill Lynch upgrading the UK housebuilding sector to neutral.
Taylor Wimpey jumped 4.8 percent to top the FTSE 100 leader board, with Persimmon and Barratt Developments up 4.4 and 2.9 percent respectively.
Adding to worries at home, however, official data showed that Britain's economic growth hit a six-month low in the three months to November as factories suffered from tough global trade conditions ahead of Brexit.
Airline Flybe plummeted 77.1 percent to a record low of 3.8 pence after a heavily discounted 1 pence-per-share buyout offer from a consortium of Virgin Atlantic, Stobart and Cyrus.
Stobart jumped 7.2 percent after the news to top the mid-cap winners.
Retailers continued to upset the markets, with AIM-listed fast-fashion retailer Quiz tanking 32.5 percent to a record low after a revenue warning following disappointing Christmas sales.
Suits specialist Moss Bros also said the period ahead would be "extremely challenging", but its shares firmed as analysts took comfort from strong e-commerce sales.
Debenhams plunged 18.8 percent in high-volume trading. Investors had forced the department store group's CEO off the board and the chairman out of the company on Thursday after another plunge in sales.
UDG Healthcare slumped 7.7 percent to be the biggest mid-cap faller after Jefferies downgraded the stock and said the healthcare services provider's preliminary expectation for the year "does not sound attractive".
(Reporting by Muvija M; Additional reporting by Pushkala Aripaka in Bengaluru; Editing by Raissa Kasolowsky and David Goodman)
By Muvija M