Analysts and economists in the City of London are starting to virtually rule out the prospect of the UK leaving the European Union without a deal after a week in which two crucial developments in British politics seemingly lessened the likelihood of no deal.

This week, analysts JPMorgan and Pantheon Macroeconomics both affirmed their belief that the chance of a no deal Brexit is around 10-15%, while Capital Economics said it believes the chances of no deal is "receding."

So what's happened to change the minds of the City's brightest minds, some of whom in recent months have forecast no-deal as the most likely of Brexit outcomes?

It effectively boils down to the fact that Prime Minister Theresa May was forced into a compromise that will give members of parliament the ability to both create a short delay to Brexit, and to rule out no deal in the short term.

May told MPs on Tuesday that should they reject her deal for a second time, they would be given a series of binding votes on whether to leave the EU without a deal or to delay Brexit.

"The UK will only leave without a deal on March 29 if there is explicit assent in the House for that outcome," May said in the House of Commons.

She added that if her deal were rejected for a second time, then MPs would be offered a vote on March 13 on leaving without a deal and then a vote on March 14 on whether to delay Brexit.

It is extremely unlikely that parliament will vote for no deal. Only a very small number of MPs are even willing to countenance the UK leaving the EU without a deal, a prospect which is all but guaranteed to cause large scale chaos in Britain, and wreak lasting damage to the economy.

As such, as Capital Economics' UK economist Thomas Pugh writes in a note titled "Chances of no deal receding":

"Admittedly, we are much more uncertain about the probabilities that we assign to the various Brexit outcomes than we are about what may happen to the economy in each scenario. But, for what it's worth, we think that the total probability of a no deal at some point has fallen from around 30% to 20%."

The feelings of the City can most succinctly be summed up by Karen Ward, JPMorgan Asset Management's chief market strategist for EMEA. During an interview with Business Insider this week, Ward was asked how she was feeling about the prospect of no deal.

Her reply: "Sanguine, but never sanguine to the point of complacency."