It’s ok to disagree but to deride anything you don’t like as ‘myths’ and ‘right wing’ is just not discussing a topic in good faith.
I’ve not said that increases in public spending will definitely always cause inflation. These things are contextual and 2010 to 2024 was characterised by a government committed to reducing a deficit that had been reduced from the state Labour had left in 2010.
Anyway, onto the question you posed. In short, government spending contributes to aggregate demand in the economy which will risk inflation. There are two examples that come to mind. 1) the government’s COVID response for businesses as well as individuals (along with debt holidays etc). The economy was overheating at time it should’ve slowed. 2) Quantative Easing, the headline inflation rate (CPI) remained quite low between 2010-2020, the increase of assets prices have been quite staggering. Specifically, in housing where the costs to buy a mouse and maintain a mortgage has increased significantly over that period too. Which is an outlier considering growth has slowed.