The first device, addressed to Mr Waldegrave, was sent to his family farm in Chewton Mendip, Somerset.
It was spotted by a postman and dismantled by a bomb disposal team. It is being examined at the Forensic Science Laboratory in Chepstow, while Avon and Somerset detectives have begun an investigation. The envelope had a London postmark.
Mr Waldegrave is believed to have been targeted because of his perceived lack of action in stopping the live animal export trade and for the slow progress in banning veal crates across Europe.
In January, two packages booby-trapped with razor blades were sent to Mr Waldegrave's London home. Threatening letters were posted to him after the disclosure that calves from his farm were being exported to the Continent where veal crates are common.
His farm has also been the scene of protests by animal rights activists and opponents of the Criminal Justice Act.
Mr Waldegrave's wife Caroline, owner of the Pru Leith School of Cookery in London, also angered animal rights campaigners by writing about the merits of Dutch veal, produced in crates.
William Waldegrave last night dismissed the bombing attempt as "stupidity".
Mr Waldegrave said: "It is ironic that the British Government, which is leading the way to higher welfare standards in Europe, should be subject to this sort of thing."
"This won't have the slightest affect on policy because in a free society there are always going to be a few eccentrics who do daft things like this, and ministers in all countries just have to get used to it."
Animal rights groups moved swiftly to distance themselves from the extremists.
Peter Stevenson, Compassion in World Farming's political and legal director, said: "We are utterly appalled at this kind of action or any violent protest for that matter. People like this are ruining our protests by eroding public sympathy for a perfectly legitimate cause.
The second bomb, addressed to Mr King, now a backbencher, was intercepted at Westminster.
A third was intercepted and made safe in the postroom of Ethicon, which makes sutures, at a plant in Edinburgh.
Staff at the factory, which includes an animal testing laboratory, were evacuated while the bomb was made safe.
"There's no reason for us to be a target. We test our products for efficiency. We do not consider ourselves to be doing anything other than the most rudimentary tests," said Graeme Crawford, a spokesman for the company.
The final device was destroyed in a controlled explosion at the Alaska Fur Company in Glasgow's city centre.