* UK warns Islamic State trying to attack infrastructure
* Plans to double spending on cyber security
* Osborne says UK will hit back if attacked (Recasts, adds details)
By Michael Holden
CHELTENHAM, England, Nov 17 (Reuters) - British spies are building elite cyber offensive forces to strike at Islamic State fighters, hackers and hostile powers, finance minister George Osborne said on Tuesday after warning militants wanted to launch deadly digital attacks.
Islamic State was trying to develop the capability to attack British infrastructure such as hospitals, power networks and air traffic control systems with potentially lethal consequences, Osborne said.
In response, Britain will bolster spending on cyber defences, simplify its state cyber structures and build its own offensive cyber capability to attack adversaries.
"We will defend ourselves. But we will also take the fight to you," Osborne, Britain's second most powerful politician after Prime Minister David Cameron, said in a speech at Britain's GCHQ eavesdropping agency.
"We are building our own offensive cyber capability - a dedicated ability to counter-attack in cyberspace. When we talk about tackling (Islamic State), that means tackling their cyber threat as well as their guns, bombs and knives."
Britain's new cyber attack forces will be run jointly between GCHQ and the Defence Ministry and will target individual hackers, criminal gangs, militant groups and hostile powers, using a "full spectrum" of actions, Osborne said.
GCHQ traces its history back to World War One signals intelligence with Winston Churchill as its founder and once reported to the MI6 foreign intelligence service but has since gained significant influence as one of the world's pre-eminent eavesdropping agencies.
One of the most secret spy agencies in the world, its existence was only officially recognised legally by Britain in the 1990s.
After last Friday's Paris attacks, which killed at least 129 people and were claimed by Islamic State, Britain said it would boost staff at its domestic MI5 security service, MI6 and GCHQ by about 15 percent.
Osborne said public spending on cyber security would be almost doubled to a total of 1.9 billion pounds ($2.9 billion)over the period to 2020, saying the decision to ramp up cyber defence funding had been taken before Friday's bloodshed in Paris.
Islamic State was already using the internet for propaganda, to radicalise people and for planning purposes, he added
"They have not been able to use it to kill people yet by attacking our infrastructure through cyber attack," he said. "But we know they want it and are doing their best to build it.
GCHQ was currently monitoring cyber threats against 450 companies in aerospace, finance defence, energy and telecoms sectors, while the number of cyber national security incidents had doubled to 200 a month since last year, he said.
A new national cyber security plan drawn up by the government would feature a dedicated force to ensure faster and more effective responses to major online attacks. The force would be based at GCHQ in Cheltenham, southwest England.
Other elements of the plan included possible cooperation between internet service providers, with help from the government, to fend off malware attacks and block bad addresses used against British internet users, as well as a new institute to train coders, Osborne said.
British broadband provider TalkTalk suffered a cyber attack in October which affected 157,000 customers. This month, Britain and U.S. authorities carried out a drill with leading banks to test their response to a cyber incident in the financial sector.
"The experience in the last month of TalkTalk shows how cyber attack can suddenly go from a theoretical risk to a massive business cost," Osborne said. (Additional reporting by William Schomberg; editing by Stephen Addison and Guy Faulconbridge)