The FTSE 100 Index was 74.4 points off at 6710.52 - building on a 60-point fall last Friday. The end-of-session finish was the lowest since 10 March.
It came after weekend talks between Greece and international creditors about freeing up bail-out funds failed to produce agreement.
Prime minister Alexis Tsipras told a Greek newspaper that his government had rejected demands from eurozone and International Monetary Fund (IMF) members for a new round of pension cuts.
Tony Cross, market analyst at Trustnet Direct, said: “The direction of stock markets this week is likely to be dictated by macro events. While a growing number of commentators now believe a Greek exit from the eurozone is all but inevitable, long-term it could bring greater stability to the economy both within the central European block and for Greece itself. The big question for investors though is just how much pain are they willing to take in the short-term as Greece goes through a potentially messy divorce?”
In stocks, budget airline easyJet was among the top-flight fallers after a downgrade from brokers at RBC Capital.
It cut the stock to an underperform from outperform and slashed its target price to 1,500p from 2,000p on fears of lower second half profits and a winter squeeze. Shares dipped 36p, or 2 per cent, to 1,550p.
British Airways owner International Airlines Group was down 9.5p at 508.5p.
Asia-focused bank Standard Chartered topped the fallers’ board after a downbeat note from brokers at Jefferies concluding that corporate non-performing loans would rise modestly in 2015. Shares fell more than 2 per cent, or 26p, to 1,038p.