Against expectations, the Bank of England has decided to keep the base rate at 0.5 per cent.
In addition, the quantitative easing programme will not be expanded.
The Monetary Policy Commitee voted by a majority of 8-1 to maintain bank rate at 0.5 per cent.
The Committee also voted unanimously to maintain the stock of purchased assets financed by the issuance of central bank reserves at £375 billion.
However, the Bank says "most members" expect monetary policy to be loosened in August.
Markets were pricing in an 80 per cent chance of a rate cut, with many expecting the Bank's QE programme to resume too.
The interest rate has not moved since March 2009.
In a speech last month, after the EU referendum, Carney says that the economic outlook for the UK had "deteriorated" following the vote.
At the time, he said the bank would cut interest rates or restart QE this summer. He said an initial assessment would be published this week, while a full assessment and new forecast will be published with the August inflation report.
Mike Bell, global market strategist at JP Morgan Asset Management, says: "Since the vote, UK consumer confidence, hiring intentions, business expectations and the construction outlook have all fallen. The declines in consumer and business confidence put the UK’s economic recovery at risk with growth likely to be meaningfully weaker than otherwise and with the risk of recession elevated.
"While the fall in sterling, combined with the rise in oil prices, will inevitably lead to a sharp increase in headline inflation over the coming year, the Bank of England will be more concerned by the downside risks to economic growth than the upside risk to inflation."
Experts think it is unlikely the Bank will cut rates below zero, with Bell saying the BoE will be "reluctant to take interest rates into negative territory" because of the impact it would have on banks.
Ahead of the announcement Fidelity International fixed income manager Ian Spreadbury said it would be a mistake for the Bank of England to cut rates today.
He said: “I think if Mark Carney does [cut rates], what are you achieving? Are you really achieving growth? I think there’s a bigger risk that they’re just exacerbating the rich-poor divide and just encouraging people to save more."