Lord Dannatt, the former chief of the general staff, said air strikes had “failed” to stop the advance of the extremists and urged Parliament to debate deploying up to 5,000 soldiers.
The fundamentalist group, responsible for the beheadings of several British hostages, has recently made gains in the Middle East by gaining control of the ancient town of Palmyra, in Syria, and the Iraqi city of Ramadi.
Lord Dannatt said: “In light of this terrifying scenario, how much longer can Britain and the US continue to show such a lack of commitment to defeating IS militarily? Their default option of air strikes and limited assistance to indigenous forces has failed thus far.
“We have now reached a point when we must think the previously unthinkable and consider that British troops, acting as part of an international coalition, may be required to mount a ground campaign in Iraq and Syria.
“I am no gung-ho general who says ‘just send the boys in and don’t worry about the body bags’, far from it, but faced with such a lethal and uncompromising enemy as IS – and with the lack of political and diplomatic solutions at our disposal – we can no longer rule out ‘boots on the ground’.”
Writing in a Sunday newspaper, the retired general said political leaders had avoided the “politically toxic” question during the general election campaign but David Cameron should begin planning.
Lord Dannatt admitted there would be political challenges, including obtaining a United Nations Security Council resolution with the backing of China and Russia, while Syrian president Bashar Assad should be removed from office but “granted sanctuary in another state”.
Conservative former defence secretary Liam Fox said boots on the ground would require the United States as the “prime mover”.
He said: “I think that is out of the question under the Obama presidency. I think even if he were to be persuaded that it was the right thing to do, and I’m not sure at all that he is, then I don’t think he would be willing in the last year or so of his presidency to have that as his legacy.”
Defence Secretary Michael Fallon announced in March two RAF Sentinel surveillance aircraft had been deployed to the region to operate alongside Tornado strike jets and Reaper drones that have been carrying out air strikes against Islamic State (IS) targets in Iraq.
The UK has sent around 75 military trainers and headquarters staff to provide instruction in small arms use, infantry tactics and medical skills as part of a US-led programme.