Stronger energy shares help FTSE to set one-week high

* Blue-chip FTSE 100 index up 0.7 pct

* Shell (LSE: RDSB.L - news) leads energy shares higher

* Earnings reports also help market

By Atul Prakash and Liisa Tuhkanen

LONDON, July 30 (Reuters) - Britain's top share index rose for a third straight day on Thursday to a one-week high, with energy shares leading the market higher following stronger oil prices and a rally in Shell after it announced jobs and spending cuts.

The blue-chip FTSE 100 index was up 0.7 percent at 6,679.59 points by 1117 GMT after rising to a one-week high of 6,687.81 points. It closed 1.2 percent higher on Wednesday after rising 0.8 percent in the previous session, when it snapped a five-day losing streak.

The UK Oil and Gas index surged 3.2 percent, the biggest sectoral gainer, after oil prices rose following a larger-than-expected fall in U.S. crude and gasoline stocks and figures showing a decline in U.S. oil production.

Royal Dutch Shell (Xetra: R6C1.DE - news) led the energy sector higher, with its shares rising 4 percent after the company said it would axe 6,500 jobs this year and step up spending cuts. It plans to increase asset disposals to $50 billion between 2014 and 2018 as it pushes ahead with its proposed $70 billion acquisition of BG Group.

Shares (Berlin: DI6.BE - news) in BG Group (LSE: BG.L - news) also jumped more than 4 percent.

"Shell's move of cutting jobs and reducing capex has pleased investors as it's a good way of maintaining a strong dividend culture," Jawaid Afsar, senior trader at Securequity, said.

"Sentiment has also improved as its integration with BG is also going well."

The broader market also got some support from earnings reports. Rolls-Royce rose 2.2 percent despite reporting a 32 percent drop in half-year profits as the numbers came in slightly better than expected after the engine maker slashed its forecasts three times in the past nine months.

Royal Bank Of Scotland (LSE: RBS.L - news) gained nearly 1 percent after reporting a modest rise in second quarter profits, while asset manager Schroders (LSE: SDR.L - news) gained 2 percent after posting forecast-beating first-half profit, helped by strong demand for its fixed income products.

On the downside, engineering and support services firm Babcock dropped 3.9 percent, the biggest decliner in the FTSE 100 index, with revenue from the defence and security division coming in lower in the first half of the year.

BT Group (LSE: BT-A.L - news) fell 1.8 percent despite posting first-quarter revenue and core earnings in line with forecasts.

"Results were in line with expectations but Global Services performance was disappointing despite all the cost cutting. Broadband disclosure was also slightly weaker than expected," Brenda Kelly, analyst at London Capital Group, said. (Additional reporting by Sudip Kar-Gupta and Tricia Wright; Editing by Alison Williams)