From Gavin Longmuir in the comments:
From a civil engineering perspective, as one of the profs at Grayvington U might say, restoration of a crumbling old tower is akin to walking on eggshells — preserve the exterior façade while rebuilding and strengthening the interior. A single mistake, the tower falls down, and the civil engineer has to spend the rest of his career building mud huts in Zambia.
If the engineering contractor has to disrupt an exquisitely planned schedule to do whatever has to be done to make it possible to ring the bells safely, and then has to undo all of that temporary work and get back to the original plan — then 500K does not sound like an improbable number.
500k can easily be raised, though. Just don’t expect Parliament and the civil service to take the money.
My view is that if Big Ben won’t ring, then hire some massive speakers to play a bell sound, and let the whole of London hear it.
Update: More on the Big Ben restoration project here. Surprise quote:
MPs were told the new budget is looking set to hit £80million, nearly three times the original £29million budget when Parliament signed it off in 2016.
A government project that is almost three times the original budget? But that never happens, right?