Using Japanese maths:
KIX took 7 years to build, initially for one terminal and one runway, don't have history, but current throughput is 13.5m, clearly below terminal capacity. We're in same ballpark as BHX. Original cost $20bn - runway 2 since added.
BI is at least 4x this in terms of terminal size + 4 runways. However, KIX went first, and was probably more of an engineering challenge compared to a partially reclaimed / island / estuary location. However, ultimate objective (claimed) is still 10x current KIX throughput. So when it comes to cost, can this really get done for less than $40bn / £25bn (2x KIX?).
Now we haven't built any mega airports lately, but we are proposing to build approx 170k of high speed railway, to be ready by 2026. This still has to go through parliament, then a detailed design process. Say Liz signs it off in 2014, and we start building in 2016 + two years (yes two years) of testing at the other end.
So still 8 years. Again, just as they later pioneered offshore airports, the Japanese pioneered high speed trains, long before we had sophisticated CAD modelling, not to mention more powerful machinery. The Tokaido Shinkansen, opened in 1964, took just 5 years, but at 515k is around 3x longer than HS2.
So even 60 years before HS2 gets opened, the Japanese were building 103km / year compared to our proposed 21k / year - so 5x as fast.
By that logic, Boris Island could take 7 (KIX) x 5 (x slower) x 4x (as large) = 140 years.
I hope it is a little bit quicker than that!