* FTSE 100 up 0.8 pct in early trade

* CIT Group $3 bln rescue boosts sentiment

* Rightmove says UK property price falls have bottomed

By Harpreet Bhal

LONDON, July 20 (Reuters) - British shares climbed in early trade on Monday, on course to rise for the sixth straight day, tracking gains in Asia as a last-minute $3 billion rescue of U.S. CIT Group Inc CIT.N lifted sentiment.

By 0811 GMT the FTSE 100 .FTSE rose 36.79 points, or 0.8 percent at 4,425.54, after posting its best weekly rise since early January at Friday's close.

UK stocks were lifted after shares in Asia rose to a 10-month high, the best performance since the collapse of Lehman Brothers, as strong U.S. corporate earnings spurred optimism about the pace of global economic recovery.

Banks were the biggest gainers on the UK index, with Barclays (BARC.L: Quote, Profile, Research), HSBC (HSBA.L: Quote, Profile, Research), Lloyds Banking Group (LLOY.L: Quote, Profile, Research) and Royal Bank of Scotland (RBS.L: Quote, Profile, Research) rising between 1.2 percent and 5.9 percent.