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The FTSE 100 was 31.47 points higher at 6,622.11 by mid morning, while the more UK-focused FTSE 250 was up 174.24 points, or 1.1%, at 16,351.99.
Mining shares were among the top risers, with both Anglo American and Glencore up by more than 4.5%.
Property shares continued to recover, with Barratt Developments up 3.1%.
Shares in property-related companies have seen big falls since the UK voted to leave the EU, although a partial recovery was sparked last week after a note from UBS suggested the sell-off had been overdone.
Sentiment in general was also lifted by speculation that the Bank of England could cut interest rates this week.
Bank governor Mark Carney has already hinted that fresh stimulus measures could be needed following the Brexit vote, which could also mean an expansion of the quantitative easing programme.
However, the speculation of more monetary easing hit the value of the pound. Against the dollar, sterling fell 0.4% to $1.2896, and was 0.3% lower against the euro at â‚¬1.1679.
Joshua Mahony, an analyst at IG, said markets thought there was a 75% chance of the Bank cutting its key interest rate to 0.25% from 0,5% on Thursday.
"Markets typically make their moves ahead of an event, which is why we expect to see strong gains for the FTSE and continued weakness in sterling over the coming days," he said.
Rising mining shares and a continued rebound in the property sector have helped to lift the FTSE 100 index to an 11-month high.