David Cameron was warned to expect a Tory rebellion over high-speed rail. But while the government has been busy buying off cabinet ministers and local politicians with extra tunnels in Buckinghamshire, the prime minister has been blindsided by a new opponent: his own father-in-law.

Lord Astor has spoken out against the case for the HS2 rail network – a plan, he says, that is largely supported by "northern Labour MPs who relish the thought of the beauty of the Chilterns being destroyed".

The Conservative peer says the £33bn scheme, which has the personal backing of the prime minister, was a "Pooh trap" for ministers who loved grand projects. Writing in the upcoming issue of the Spectator, Astor states: "There is a perfectly viable alternative, which … would be much cheaper and faster to take effect, without destroying a whole swath of countryside, ruining the lives of thousands."

Questioning the judgment of the transport secretary, Justine Greening, and the government, he asks: "Have they not heard of Skype and the internet?"

The 4th Viscount Astor, stepfather of Samantha Cameron and chairman of the Old Berkshire Hunt, admits to a certain bias, having "ridden over the Chilterns all my life".

Greening's decision on Tuesday to press ahead with the network linking London, Birmingham, Manchester and Leeds was widely regarded as the go-ahead after years of planning, public consultation and ministerial delay. The project will deliver an estimated 40,000 jobs and has been seen by Cameron as a way to minimise the north-south divide.

However, Astor issued a stern message to Greening: "She should compare HS2 with cheaper options and look at how those savings could be spent on other transport needs."

Downing Street declined to comment on Wednesday, but Cameron is not the first recent incumbent of No 10 to see a flagship policy decried by his father-in-law. Tony Booth, father of Cherie, publicly stated that the 2003 war in Iraq was all about oil, somewhat contrary to the official position of his son-in-law, Tony Blair.

The similarities between the Eton-educated, Oxfordshire-dwelling multimillionaire Viscount Astor and the Liverpudlian actor Booth may be few, but Cameron may be reassured by the parallel. History records that Booth's intervention did not prevent Blair invading Iraq, any more than Astor is likely to stop high-speed rail crashing through the Chilterns.