Downing Street refused to comment on the allegation, but insisted that the UK's intelligence services always acted within the law.
A spokesman said: 'We never comment on intelligence matters. Our intelligence and security agencies act in accordance with national and international law at all times.'
Asked whether British agencies had been involved in spying activities against Mr Annan, Ms Short - who quit the cabinet in protest over the Iraq war - said: 'I know, I have seen transcripts of Kofi Annan's conversations.
'Indeed, I have had conversations with Kofi in the run-up to war, thinking: 'Oh dear, there will be a transcript of this, and people will see what he and I are saying'.'
Ms Short was asked whether she believed that British spies had been instructed to carry out operations within the UN on personnel such as Mr Annan. 'Yes, absolutely,' she replied.