Fuel protests in the United Kingdom - Wikipedia
This now a fairly obscure event, but it was by far the most dangerous point during New Labour's first term in office. I think Alastair Campbell has said that he was genuinely terrified that the government would fall and that it brought back memories (to the electorate) of the various crises that previous Labour governments had overseen and often been blamed for.
The trouble that the government was in, albeit briefly, can be seen in the opinion polls that were taken at the time. It was the only period between Black Wednesday in 1992 and the invasion of Iraq in 2003 that the Tories led Labour.