The slump by the blue-chip pair wiped as much as 50 points from the FTSE 100 Index, which fell by more than other European markets to finish 113.1 points lower at a five-week low of 6550.6.
The decline was on top of a loss of 100 points on Friday after a plunge in the value of Argentina's currency sparked fears of a new emerging markets rout.
Anxiety is also building over what might happen if, as expected, the US Federal Reserve later this week stages a further withdrawal of the monetary support pouring billions into the world's biggest economy.
The availability of "easy money" in the US has seen investors ploughing cash into fast-growing emerging markets to seek better returns so there is concern over what will happen to these economies when the taps are turned off.
The dollar weakened against the pound, which was up by just under 1% at $1.65 and at 1.21 against the euro.
Sentiment in London was further impacted by the performance of the two heavyweight stocks, with BG off 173p at 1082p after it downgraded its earnings guidance for this year and next.
It said too much of its gas production had been diverted into Egypt's domestic market rather than being made available for exports.
And Vodafone slid 4% or 9p to 223.5p after AT&T dismissed speculation linking it to a potential £60 billion takeover approach for the UK company.
Under takeover rules, AT&T is now prevented from making a move for Vodafone for six months, unless another party tables an offer for the UK company in the meantime.
Other fallers included Royal Bank of Scotland after its admission late in the session that it will have to set aside more than £3 billion in additional funds to cover litigation and customer compensation claims.
The sum includes an extra £465 million to cover a redress scheme for customers mis-sold payment protection insurance. Shares were 7.5p lower at 332.2p, a drop of 2%.
Fund supermarket Hargreaves Lansdown was also under pressure, down 80p or 5% to 1429p.
Pawnbroker Albemarle & Bond slumped after it said attempts to find a buyer for the business had failed, casting further doubt over the future of the company.
The stock halved by 11.25p to 8p as Albemarle said its attempts to secure a rescue were unlikely to carry much value for shareholders.
The biggest FTSE 100 risers were United Utilities up 13p at 713.5p, Severn Trent ahead 22p at 1700p, Rolls-Royce up 12p at 1184p and Weir Group ahead 17p at 2107p.
The biggest fallers were BG Group down 173p at 1082p, Hargreaves Lansdown, Vodafone and Pearson off 45p at 1126p.