This is unlikely. Every single major advanced economy with monetary independence - that is, outside the eurozone - has seen long-term interest rates fall sharply over the past two years. It is simply false to say that we have low long-term interest rates now because the deficit has been cut: projected future borrowing is now higher than before the austerity plans were announced. As theIMF says, low interest rates are the result of weak growth, here and around the world.
More broadly, there are plenty of other infrastructure projects that could be taken off the shelf. The coalition government points out that it has cut the deficit by a quarter; but two-thirds of the reduction came from cutting public investment: schools, roads and hospitals.