Mr Deadman added the use of direct-access pipes in the UK would be illegal because agencies have to obtain a warrant to get information.
The report breaks down lawful intercept requests and communications data requests for the 29 countries in which Vodafone operates for the period 1 April 2013 to 31 March 2014.
The UK government made 2,760 interception requests and 514,608 communications data requests to all mobile phone operators in 2013.
By comparison, Italy made 139,962 interception requests in total and 605,601 communications requests to Vodafone alone. In the US, Verizon said it received 321,545 requests for customer information.
Some of the figures are being disclosed by Vodafone for the first time, including those for Spain and Tanzania.
Several countries refused to reveal the number of requests they made, including Egypt, India, Qatar, Romania, South Africa and Turkey.
Mr Deadman said: 'We need to debate how we are balancing the needs of law enforcement with the fundamental rights and freedoms of the citizens.'
Shami Chakrabarti, director of human rights campaign group Liberty, said: "For governments to access phone calls at the flick of a switch is unprecedented and terrifying.
"Snowden revealed the internet was already treated as fair game. Bluster that all is well is wearing pretty thin - our analogue laws need a digital overhaul."
Sign up for CIO Asia eNewsletters.