But he added: "Far Eastern cities use towers to fund their infrastructure. Building CrossRail with only five-storey buildings on top of it is a nonsense. We will have to think of towers in terms of their social, economic and transport benefits as well as the demand factor."
CrossRail stations are planned for Paddington to Stratford in east London via Tottenham Court Road, Farringdon and Liverpool Street.
Lipton said five or six tall building proposals had been submitted for a zone on the north-east fringes of the City. CABE and EH have agreed in principle that it is an appropriate area to build a cluster of towers, but have yet to be convinced of the quality of particular submissions.
He said: "The question is, will hey be good enough? They have to be not only high quality but inspiring, like the Chrysler Building in New York."
Lipton emphasised that London would not become a city of tall buildings, and neither would any regional cities in the UK.
Sir Neil Cossons, chairman of EH, said the heritage body and CABE would carry out detailed research in the next few months into the case for building tall.
Cossons added that Ken Livingstone, the mayor of London, had proposed to review the statutory "strategic views" across London to see which might be relaxed. EH has agreed to advise him on this.
Phillip Davies, EH's London regional director, said that other iconic views of London could be added to the protected list: "We hope the view of Whitehall from the bridge in St James's Park and the view from the Serpentine in Hyde Park will be enshrined in regional planning policy in future."
CABE and EH have invited comments on Guidance on Tall Buildings by 15 October.