According to the statement in Parliament the "high speed" cost of the new line will be £1.2bn. This sounds like a case of massaging statistics and implausible.
First, the HST needs an entirely new route to accommodate the higher speeds. A conventional speed railway can be laid on unused route from Calvert to Rugby and from Old Oak Common to Northolt Junction. The railway remains operational all the way from Calvert to Marylebone, forming part of the Chiltern line commuter route to Aylesbury. Going towards London there is a connection to the GW main line south of Calvert, and another to the Oxford to Bletchley.
Second, the rolling stock costs for high speed are about double, and three times as much in the case of the special UK gauge rolling stock that will have to be used for running on both old and new lines.
Third, the energy costs are double, and they can only rise as time goes on.
Fourth, there is all that tunneling.
We could get all the extra capacity you wanted by building the GC back to Rugby, putting in a connection to the WCML, reinstating the Ashendon Junction to Grendon Underwood Junction link, restoring Northolt Junction to Paddington, electrifying Marylebone/Paddington/Oxford to Birmingham and putting all the Heathrow Express trains underground as part of the Crossrail scheme.
That would cost less than half of HS2.