Except that the UK's national debt was far lower under the last Labour government than it is currently. And austerity has never fixed anything - if you suck money out of an ailing economy, the result is further stagnation and prolonged recession. Every economist knows this, and yet still the same tired old tropes are trotted out by right wing governments and media, and still people believe them.
Of course Labour will have to borrow to fund their manifesto commitments - just as the present government has borrowed at record levels, but in their case merely to keep the economy on life support. By putting money directly into working people's pockets, for example by lifting the punitive 1% pay cap on public sector workers, Labour's policy will stimulate economic activity. This is basic Keynesian Economics - these lessons were learned in the 1930's. It's why the Roosevelt administration built the Hoover Dam for heavens sake; absolutely heartbreaking that we are having to learn it all over again.
You do not cut public spending during a recession; you borrow to invest in the lean times, and pay down the debt in the times of plenty.