Chiefly because pundits seem to agree that current government doesn't actually want the Heathrow expansion to proceed. It should be noted that the Government is not pursuing an appeal to the Supreme Court; the case is being pursued privately by Heathrow Airport itself.
The current Prime Minister, then Foreign Secretary, Boris Johnson, was conveniently absent on a trip to Afghanistan for the vote in the House of Commons that approved the third runway in June 2018. This was likely due to his previous commitments to oppose the expansion - he told supporters in his constituency that he would "lie down with you in front of those bulldozers and stop the building, stop the construction of that third runway". Because of collective Cabinet responsibility, he would have been forced to resign if he voted against the proposals.
The legal case was brought by Sadiq Khan, the Mayor of London in response to the decision, and argued that the Government, in particular the Transport Secretary, Chris Grayling, had not considered its commitments to the Paris Climate Agreement. Because this was upheld by the Court of Appeal, the Government must now show that the expansion is consistent with the commitments made - and be able to satisfy the courts of that - or repeal the act that formalised the UK's agreement to the climate accord. This would be considered quite an embarrassing option, considering Johnson's public criticism of President Trump, when the US exited the agreement in 2019.
In conclusion, then, of course it is within the ability of the UK Government to legislate to allow the third runway, however it is questionable if this is firstly, proportionate - it would require at minimum de facto exiting the Paris Climate Agreement, or secondly - what the Government actually wants to do.