A further 111 are thought to have been wounded in the strikes.
Armed Forces Minister Mike Penning revealed the figures after a written parliamentary question by Lib Dem leader Tim Farron.
He said they were an estimate because strike sites cannot be visited and assessed by the UK.
Mr Farron had asked the Ministry of Defence how many militants from the terrorist group had been killed by British forces in Iraq from 2 December 2015 to 2 December 2016.
Mr Penning replied: "During the period in question it is assessed that there were a total of 111 enemy wounded in action and a total of 1,306 enemy killed in action as a result of UK air strikes.
"The UK cannot visit strike sites and conduct detailed investigations on the ground in Iraq. Therefore the number of combatants killed and/or wounded is an estimated figure only."
The UK parliament backed British participation in air strikes against IS in Iraq back in September 2014. Just over a year later in 2015, MPs authorised air strikes against IS in Syria.
The UK has conducted more than 1,200 airstrikes in Iraq and Syria since it became involved - more than any other coalition country bar the United States.
BBC analysis has shown that in 2017, UK forces dropped bombs in Iraq and Syria on 69 of the first 99 days of the year.
RAF Typhoons and Reaper drones have been supporting Iraqi and Kurdish forces trying to liberate Mosul, northern Iraq, in recent months.

That phrase hinted both at an ideal flexible arrangement in the future and an ideal shared approach from both the UK and Irish governments, together stressing to the EU the paramount importance of doing nothing that might constitute any kind of risk to the political progress made over recent decades.
But is that seamless approach unravelling and could Brexit become a source of greater friction between the two governments?
Both the Brexit Secretary David Davis and DUP leader Arlene Foster have been fond of talking about technology as the answer to Ireland's post-Brexit problems.
Yes, they acknowledge, putting old-style customs checkpoints right on the border would be unacceptable for both political and security reasons.
However, they then go on to suggest that provided businesses co-operate with computerised trusted trader schemes, and cameras with number plate recognition capability are installed some distance away from the frontier, all will be well.
By contrast, the Irish Foreign Minister Simon Coveney has now warned that technology isn't the answer.
Instead, he argues there is a need for a wider political agreement. What does that mean?
On the BBC's Good Morning Ulster programme, Fine Gael Senator Neale Richmond hinted that the Irish favour moving customs controls to seaports and airports, rather than anywhere near the land border.
This might sound geographically sensible, but the political implications should not be underestimated.
Arlene Foster has previously said that putting a border down the middle of the Irish Sea, creating a divide between Northern Ireland and Great Britain, is something her party will not tolerate.
So long as the DUP-Conservative parliamentary arrangement survives, that is a concern David Davis and Theresa May will have to take very seriously.
But, if the DUP has the ear of the British government, then similarly as a loyal EU member state, Dublin has the ear of Michel Barnier's negotiating team.
Since becoming foreign minister, Simon Coveney has not been shy about making his differences with the UK clear.
He voiced his concern for Northern Ireland having special EU status, which contrasted with the position of his predecessor Charlie Flanagan.
Some surmised this might only have been a slip of the tongue.
However Mr Coveney's decision to let it be known he favoured a bespoke Irish Language Act (Sinn FÃ©in, the SDLP and Alliance's preference) over a hybrid bill (the DUP's suggestion) was a clear move to distance Dublin from the Northern Ireland Office's studied neutrality on the issue.
If the border after Brexit becomes a more open source of arm wrestling between the two governments, that could have consequences  - not just for the continuing UK/EU negotiations, but also for the Stormont talks when they resume in earnest in the autumn.
More than 1,300 militants from so-called Islamic State were killed by British air strikes in Iraq over a 12-month period, according to new figures.
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For months, it's been the joint mantra from both Dublin and London - that after Brexit, the border between Northern Ireland and the Republic of Ireland should be as "seamless and frictionless as possible".