If Boris Island goes ahead, then vast amounts of material will be needed to raise the runways and other structures above sea level. Some could probably be found by dredging, but probably not enough, and more likely, insufficient with the right mechanical properties. For Chep Lap Kok they found enough hard rock fill by taking the top off a (small) mountain, but there are no comparable mountains in Kent or Essex that could be beheaded.
Coincidently, there is currently a search going on for a place to excavate a long-term store for long-life radioactive waste. The favourite at present seems to be the coastal fringes of the Lake District. However, if the dump were to be moved to the south-east, the problems of where to dump spoil from the excavation and where to acquire fill for the airport island would solve each other. After all, south-east England has everything else, so why not let it have the radioactive dump as well.
On a slightly different theme, business and high-tech industry tend to locate where there are good air services, and additional air services are devloped where business and high-tech industry provide a demand. Despite short-term tweaks, the limits on capacity at Heathrow are tending to break this positive feedback loop. Either a solution will be found in less time than it would take to open Boris Island or build a third runway, or things will go elsewhere. If that elsewhere is not to be outside the UK, then there must be investment in at least one other UK hub outside the London area.
Both the midlands and north-west england, or even central Scotland, could already provide the traveller seed to support a hub. What is needed is provision and promotion of regional and long-haul services from one of those potential hubs.
Manchester is already attracting long-haul operations by non-uk airlines, so perhaps with a relatively small investment the two runways at Manchester could provide the UK with the capacity and flexibility the third LHR runway would have produced without the expense and disturbance of building Boris Island.