The benchmark FTSE 100 index closed up 1.18%, or 71.58 points, at 6,146.10.
Whitbread shares lost 1.4%, the biggest faller on the FTSE, after it said it would have to cut costs and raise prices to pay its staff the new government recommended Living Wage.
Housebuilders Redrow shares rose 1.9%. Profits rose 53% helped by government's Help to Buy subsidy for some buyers.
Shareholders in fellow builder Berkeley were also in the money after its shares climbed 2.3% on news it was on track to meet its profit targets.
Outside the top 100, Punch Taverns' shares were up 3.2% after it said it would sell its 50% stake in its UK-based drinks wholesaler for Â£100.7m.
On the currency markets, the pound rose 0.65% against the dollar to $1.5373 and also gained 0.45% against the euro to â‚¬1.3738.
(Close): London's leading shares rose for a second day, led by mining firms Glencore and Anglo American.