This was front page news here (aside from those tabloid papers that just had stuff about football). Here is the BBC analysis - US drops immunity request

This concludes: "What is still not clear is how far the US will go to carry out its threat to block future UN peacekeeping operations."

I imagine the UK government, which had been planning to vote for extending the immunity, must be very pleased about being let off the hook. With stories continuing to appear every few days in the papers, and in broadcast media, detailing further accounts of torture and abuse of prisoners in various places, it would have been excruciatingly embarrassing for the government to vote for further immunity - and for different reasons highly embarrassing not to.

There has never been any attempt by any other country to secure thius kind of immunity agreement. In fact, the US has, by one method or another, persuaded over 80 countries to sign bilateral agreements giving its citizens immunity from normal legal sanctions against war crimes, in practice it is unlikely this will make much practical difference.