it is reasonable to expect

Is it?

The US economy is hugely different from ours and had a worse starting base in terms of infrastructure.

How will, for example, a stimulus of that amount boost the financial services industry that is the backbone of the British economy? It's fine if you have large-scale primary and secondary manufacturing that benefits greatly from increased infrastructure like the US does, but the UK doesn't.

If we could somehow obtain £500bn on favourable terms from somewhere, to say that we could apply the same approach applied to the USA and get results is questionable.

I don't doubt that a plan for infrastructure spending is a good way to go when borrowing is this cheap (although it would have to be tailored to our economy), I doubt whether a) raising that money is at all possible in the short-to-medium term and b) whether that much money is needed for a Keynesian infrastructure programme in the UK.

Personally I reckon JC has just plucked that number out of the air to one-up Smith and knows his supporters will lap it up (I mean this 'costing' plan is so vapid that it might as well not exist, compared to Smith's costed policies).