The Parliament Square scheme, which was granted planning permission last September, is now the focus of an Early Day Motion set up by MPs who are petitioning government to halt the refurbishment.
It goes on to state that the building was restored and refurbished 'as recently as 1989' and calls for the government to think of an alternative location for its Supreme Court.
It continues: '[The House] calls on the government either to house the Supreme Court in this building with minimum alterations or bow to the substantial body of informed opinion, both legal and architectural, that believes a new supreme court should be housed in a distinguished new building specifically commissioned for the purpose with the Supreme Court in the meantime operating in the accommodation used by the law lords.'
The motion is being strongly supported by campaign group SAVE Britain's Heritage, which recently published a book emphasising what it deems to be unnecessary refurbishment work.
SAVE secretary Adam Wilkinson said: 'We are very pleased that parliament is putting this forward, and we want to encourage people to get their MPs to sign up.'
Those to have already signed the petition include high-profile Tories Peter Bottomley and Nicholas Winterton, as well as über-Blairite Frank Field.
'There are currently names in their tens, but we are hoping to have that number up into the hundreds soon,' added Wilkinson.