Greece's parliament began on Monday to debate measures to increase taxes and cut fiscal spending, approval for which is needed for the European Union and International Monetary Fund to disburse the fifth tranche of Greece's 110 billion euro ($158 billion) bailout programme.
The FTSE 100 index closed up 24.62 points, or 0.4 percent at 5,722.34, regaining the psychologically important 5,700 level.
It is fair to say sentiment remains cautious ... However, as we have seen over the last week, buyers are happy to move in on weakness for the FTSE 100 below 5,700, said Will Hedden, sales trader at IG Index.
If markets can get through the Greek vote and avoid a sustained move below this level, investors may start to see the beginning of the end of the two-month slide that has dogged markets, Hedden said.
Banks were higher as a sector, buoyed mostly by gains in global heavyweight HSBC , up 0.6 percent, while emerging markets specialist Standard Chartered added 1.4 percent ahead of a trading update on Tuesday.
U.S. blue chips were up 0.7 percent by London's close, rebounding from three sessions of losses as financials gained on Greek debt crisis resolution hopes.
Michael Hewson, market analyst at CMC Markets remained cautious. Upside pressure looks likely to remain contained ahead of this week's Greek austerity vote, he said.
Energy issues provided the main support for blue chips, led by BG Group , up 2.2 percent after signing a new co-operation agreement with Bank of China.
The deal allowed for up to $1.5 billion of new funding options to support the group's growth programme.
Miners also moved higher, with sentiment helped by a bullish note after HSBC upgraded ratings for Anglo American , Antofagasta , BHP Billiton and Vedanta Resources.
Vedanta also benefited as Cairn Energy cut the price for its acquisition of a 40 percent stake in Cairn India by around 5 percent, with the deal now to complete in two tranches.
United Utilities was the top FTSE 100 riser, adding 3.3 percent, while Severn Trent gained 2 percent as the sector benefited from a bid move for Northumbrian Water.
Northumbrian was the top FTSE 250 gainer, jumping 8 percent, after Chinese group Cheung Kong Infrastructure confirmed it was assessing a cash offer for the utility.
On the downside, drugmaker AstraZeneca shed 1.1 percent after its experimental diabetes pill, dapagliflozin, was associated with breast and bladder cancer, as well as more cases of infections, in a late-stage clinical trial.
RBS cut its target price for AstraZeneca to 2,825 pence from 3,175 pence after reducing estimates to remove dapagliflozin.
Peer GlaxoSmithKline lost 0.7 percent, with the drugs sectors the biggest drag on the FTSE 100 index.