"..there is nothing progressive about spending more on debt interest repayments than spending on the future of educating our children."I suspect it's an argument we'll hear repeated quite a lot because it has all the hallmarks a good bit of propaganda, it's short ,catchy, repeatable and has a kind of intuitiveness about it. The problem with it is that it doesn't have much merit as an effective policy.
Even if we disregard arguments about the zero lower bound, multipliers and the economic dividends from investment in things like infrastructure (and I don't think we should) there's still the plain simple maths of it all. According to the 2015 budget, total managed expenditure is £743bn, debt interest is £46bn (or £34bn if you count the APF), paying off every penny of debt interest would only allow us to increase spending by 6.5%.
More to the point, reducing debt by any serious amount would take a considerable amount of time. If we start from a debt of 90.6% of GDP, assume a 1% surplus and nominal GDP growth of 4%, it would for example take 13 years to half the outstanding national debt (as a % of GDP, another aside would be that running a 1% deficit would still see debt reduced by 29%). It would take a long time to see even small dividends from reducing the national debt.
It may be a good sound bite, but it's just not in any way sensible policy.
Update 22/6/15: Jonathan Portes posted a link on twitter to a more academic take on this subject at Vox EU.