The proposal has triggered a storm of protest from the Opposition and teachers' organisations.
Mr Patten delighted Aylesbury Conservative Association on Friday night by suggesting: 'I would like to see the Union flag flown with pride by our schools and public institutions.
'It is common in Western nations for national flags to be flown in schools, either permanently as in the USA, or on certain public occasions as in schools in many other OECD countries, including France, Italy, Australia and New Zealand. Why don't we follow suit?'
His proposal took the Department for Education unawares. A spokesman said flying the flag was 'entirely a matter for schools'. Schools in Wales, Scotland and Northern Ireland are outside Mr Patten's jurisdiction.
Last night, in an unusually brazen move for a senior Cabinet minister, Mr Howard contacted the Press Association news agency to echo Mr Patten's idea. He said: 'I have always been amazed at the extent to which other countries respect their flags while we largely ignore ours. One of the causes of our social problems is the lack of respect for authority which has become so widespread.
'Our flag symbolises the national heritage of which we should all be so proud. Respect for that national heritage is something around which the whole country should unite and respect for our flag would be a good way to start.'
Nigel de Gruchy, general secretary of the 190,000-strong National Association of Schoolmasters/Union of Women Teachers, dismissed Mr Patten's idea as 'at best barmy and at worst in some areas downright dangerous'.
He said: 'It is difficult to take seriously and will be seen as an attempt to deflect attention from the Government's many failures in education.'
Ann Taylor, Labour's shadow education secretary, said: 'The idea that you can counter racism simply by raising flags is totally unrealistic.' She accused Mr Patten of echoing the language, tone and rhetoric of the British National Party.
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