Sounds like a lot of nonsense to me, apologies if this sounds negative. You appear to suggesting a massive nationalisation/public ownership programme. No political party capable of being in government favours such a course of action.
Who would buy these bonds? Can the government, at present, afford to pay 4% and put up 40%? What if interest rates rise (in the long term they can hardly fall)? How will 4% look if interest rates are higher?
Why would the government be inclined to do all this when the private sector will finance Heathrow expansion?
Well that can be done in the way they did with "Railtrack" in which it was a nationalization in all but name for a start, which we also did with 2 of our biggest banks, also you have to remember that we still have airports that are owned by government authorities in this country (remember most European states and even the USA have state owned airports).
Also the government is effectively interfering in the running of our "private" airports by the actions they have done (like they do with the railways)
As for who would buy those bonds, well it could be savers (who suffering from the fact we have a low base rate) and maybe investors (if they are the sort who invest in long term projects)
Remember, the 4% figure I have given is a example, the final one will depend on many factors (I based it on the rate the government borrows)
As for if the government can afford the 40%, well they could, but only if they changed the way they run things (tax evasion and aviodance for a start, maybe issuing WW2-style "war" bonds to the general public)
Lastly, I am only suggesting taking this course of action, if they cannot find the political will to expand LHR
A 4-rwy LHR would need to be on segregated mode: two rwys for takeoffs, two rwys for landings, using alternation with a changeover daily at 1500 to allow some quiet for those under the flightpath. Those with quiet in the morning, would have quiet in the afternoon the next day and vice versa and so on.
The trouble is that 4 runways is the bare minimum to cope with both current traffic and allow for growth, we need to make the most of our runways (in return for further limitations of noisy aircraft) and thus meaning allowing all to be used simultaneously, now if we get the political will to allow a 5th and 6th runways (there is space without knocking down too many homes) then it might be possible to allow some slack
It doesn't take this long to construct two rwys.
Its not just the runways though, you also need to build more terminals to cope with the extra traffic and those take around 5 years to build