* UK to give counter-terror, intelligence aid to Algeria
* Considers giving more military assistance to France
* But is cautious, won't intervene militarily in Africa
By Mohammed Abbas
LONDON, Jan 21 (Reuters) - Britain said on Monday it would increase counter-terrorism and intelligence aid to Algeria and consider giving more help to France to fight Islamists in Mali, but ruled out any prospect of direct British military intervention in Africa.
Prime Minister David Cameron last week warned of the need to tackle a "large and existential terrorist threat" from different parts of the world. But a wariness about getting bogged down in another Afghanistan-style conflict may be restraining Britain.
Addressing parliament after last week's hostage-taking and siege in Algeria in which 37 foreigners - including at least three Britons - were killed, Cameron said a "patient, intelligent, but tough" approach was the best way to defeat terrorism.
"We will contribute British intelligence and counter-terrorism assets to an international effort to find and dismantle the network that planned and ordered the brutal assault," he said, referring to the hostage crisis.
Battling to slash a big budget deficit and now trying to slim down its armed forces, Britain can ill-afford another major military intervention. It is preparing to withdraw its troops from a long and costly mission in Afghanistan in 2014.
Cameron emphasised the "long-standing and deep" root causes of terrorism and pledged to help bolster democracy and the rule of law in places at risk of Islamist militancy.
Aside from participating in the U.S.-led mission in Afghanistan, Britain was also the United States' main ally in the 2003 Iraq war.
"I think we've learned lessons from Afghanistan and Iraq - you can get yourself into something and find it's very difficult to get out," said Eric Grove of the University of Salford's international security and war studies department.
The U.S. response to the Algeria crisis has so far been cautious and relatively low key.
Cameron said North Africa was becoming a "magnet for jihadists" and experts fear it could eventually become a springboard for attacks on the West, drawing comparisons with al Qaeda's use of Afghanistan as a safe haven.
However, with mixed results at best after more than 10 years of fighting Taliban Islamist insurgents in Afghanistan, the question of how to constrain militant Islam remains fraught.
"The concern is - similar to Syria - that you end up with a type of Afghanistan ... in the region, where, out of reach of the West, a very strong Islamist culture embraces an al Qaeda narrative," a senior Western intelligence source said, referring to Syria's civil war where jihadists have become prominent among rebels fighting to overthrow President Bashar al-Assad.
"But there is a huge dose of uncertainty on how the situation develops. The question is: do you just let it all happen or do you do something? And then what do you do?"
NO MALI INTERVENTION
Jihadist militants asserted that their attack on a natural gas complex in the Algerian desert was in response to French military action against Islamist insurgents in neighbouring Mali. But experts say the scale and sophistication of the attack indicate it was planned earlier.
Perceptions of a link between the Algeria hostage crisis and the French military mission had raised expectations that Western powers could increase their involvement in the Mali intervention, including providing combat troops.
Cameron's spokesman said Britain had pledged "tens, not hundreds" of troops to a European Union mission to train Malian government forces but he ruled out direct military intervention.
The prime minister instead pledged to consider increasing military aid to French forces. Britain is already providing France with two C-17 military transport aircraft for Mali.
"We'll be looking at other transport and surveillance assets that we can let the French use to help them in what they are doing," Cameron said. The government's security council is to discuss the issue on Tuesday.
More broadly, Cameron said he would use Britain's presidency of the Group of Eight industrialised nations this year to ensure the issue of terrorism and the Western response to it is "at the top of the agenda".