The list includes at least 12 bomb-makers who studied electronics at British universities.
They are now regarded as some of the most dangerous terrorists on the planet.
Special forces have been told to “use whatever means possible” to stop them leaving Iraq.
“The race is now on to kill or capture those who are left”
Any British jihadis captured alive will be handed over to the Iraqi authorities, tried and possibly executed if found guilty of terror offences.
The order was issued after intelligence suggested hundreds of British terrorists are attempting to return to the UK.
One senior source warned: “Foreign fighters serving with IS have been told to return home and carry out attacks.
“The race is now on to kill or capture those who are left.”
The SAS have been told to focus on targeting 200 senior Islamic State members who pose a direct threat to the UK.
It is understood that the British and US special forces have a series of hunter-killer teams under orders to eliminate the high-value targets.
Iraqi and Kurdish forces have closed in on Mosul – the headquarters of IS in Iraq – and are expected to capture the city within weeks.
The Iraqis have been advised by members of the SAS and US special forces throughout the campaign.
They fear the Islamist killers could attempt to carry out a wave of Paris-style massacres.
The kill list has been drawn up from intelligence provided by MI6 and CIA agents operating inside towns controlled by IS.
She vowed to behead Christians with a knife and is known to be active in Islamic State’s recruiting team.
Sources said that Jones, from Chatham, Kent, is regarded as a senior figure within the group and her links with the UK make her a major threat.
Hundreds of British nationals left the UK to fight in Syria as part of the Islamic State group and at least 60 have been killed.