Following the 9/11 attack in 2001, masterminded by the Al-Qaeda leader Osama Bin Laden, the US Government launched Operation Enduring Freedom on 7 October 2001 to target terrorist organisations, the start of what was to be a 20-year war, the longest in US history, surpassing the Vietnam War by 6 months.  The war would focus on both Iraq and Afghanistan who were seen as active supporters of terrorist operations.

In February 2003, the US Secretary of State asked the UN Security Council to give the go ahead for military action to be taken against Iraq, due to what was seen as its continued support of terrorist activities and its 'possession' of Weapons Of Mass Destruction (WMD).  As a result, at dawn on 20 March 2003, a coalition of 30 countries invaded Iraq on Operation Iraqi Freedom (Op TELIC to the UK Force).  By May, the iraqi Army had been defeated and Saddam Hussein's regime overthrown.

Key events in the war were The Battle of Nasriyah (city secured on 24 March). The Battle of Najaf, which began on 26 March with the city being secured on 4 April.  The Battle of Basrah saw UK 7th Armoured Brigade forcing their way into Basrah around 6 April after coming under constant attack.  The 3rd Battalion of the Parachute Regiment cleared the old quarter of the city, where it was difficult to use vehicles.  Full entry into Basrah was finally achieved after 2 weeks of fierce fighting, including a tank battle, when the Royal Scots' Dragoon Guards destroyed 14 Iraqi tanks on 27 March  Elements of UK 1 Armoured Division then began the advance north to around Al Amirah on 9 April.

A major pause in the war then occurred near Karbala, due to Coalition Forces meeting fierce resistance from Iraqi troops defending key cities and bridges across the Euphrates River: threatening to interdict major Coalition supply routes.  Eventually, the 101st Airbourne Division secured Najaf and Karbala to prevent further Iraqi counter attacks.  During the Battle of Karbala, the Iraqis saw the Karbala Gap as a key approach to Baghdad and it was defended by some of the best units of the Iraqi Republican Guards, whose forces suffered heavy losses from Coalition air attacks.  The Battle of Baghdad was the final battle with fighting ceasing on the afternoon of 12 April with the fall of Saddam Hussein's regime and his subsequent capture and execution later that year.

UK forces made up some 25% of the Coalition Forces:

       5,000 Royal Navy and Naval Auxiliary Personnel

       4,000 Royal Marines

       26,000 British Army Personnel

       8,100 Royal Air Force Personnel

       19 Warships

       14 Royal Fleet Auxiliary Vessels

       15,000 Vehicles

       115 Fixed Wing Aircraft

       Almost 100 Helicopters.

Op TELIC was the largest deployment of UK forces since World War II,  Sadly 179 UK personnel were killed between March and July - 136 in hostile action.

Meanwhile, in Afghanistan, the war would take on many guises, but would see widespread insurgency against the Government and Coalition forces.  Insurgents from The Taliban and other Islamist groups waged asymmetric warfare, fighting a guerilla war and mounting suicide attacks against urban targets, as well as reprisal attacks against what they saw as Afghan collaborators.  As a result, the Coalition sent a major influx of troops with a clear and hold strategy, peaking in  2011 when approximately 140,000 foreign troops were operating under ISAF Command.

On 28 December 2014, NATO formally ended Combat Operations in Afghanistan and transferred full security responsibility to the Afghan Government, who were unable to irradicate the Taliban leading to peace talks with a deal being agreed in February 2020, under which all foreign troops would be withdrawn by 2021.  On 30 August 2021, the final military departed Afghanistan.

Overall, it is estimated that between 176,000 and 212,000 people, including 43,318 civilians were killed in Afghanistan and related wars in Northern Pakistan.

As of 22 February 2020, there had been a total of 475 fatalities of UK personnel, including MOD civilians - the peak being between 2009 and 2011.  Of those 475 deaths, some 404 were classed as killed in hostile action.  The British Army saw the heaviest losses with 362 fatalities, typically those killed were aged between 20 and 29.

2,116UK personnel were admitted to UK Field Hospitals and classed as wounded in action.

4,529 personnel were admitted to UK Field Hospitals due to disease and non-combat injuries.

Of those admitted to UK Field Hospitals, 293 were categorized as Very Seriously Injured and 288 were categorized a Seriously Injured.  Some 6,663 personnel were aero medically evacuated as a result of their injuries.

Sources:

Wikipedia

UK Government Reports and Records