Ministers have decided to speed the abolition plan after consultation found support running at more than 90 per cent for new pet "passports".
An independent review of the law recommended last year that Britain's long-cherished reputation as a rabies-free country could be maintained by a European-style system of vaccination and monitoring.
The review's chairman, Professor Ian Kennedy, warned that the changes could take more than three years, but it emerged yesterday that the Government is now keen to implement the measures sooner.
The Minister of Agriculture, Nick Brown, has told the RSPCA that secondary legislation rather than primary legislation could be used to effect the changes.
Animal welfare groups had worried that a shortage of parliamentary time would mean the plans would be delayed if a Bill was needed.
Lawyers at the Ministry of Agriculture, Fisheries and Fod are assessing the idea. An announcement is likely in the next few weeks that quarantine laws will be ditched by the end of this year or early 2000.
A pilot scheme will be set up to prove the virtues of pet "passports", a system that assigns documents to dogs and cats to guarantee they have been vaccinated. More than 5,000 dogs and 3,000 cats pass through quarantine in the UK every year, costing owners up to pounds 1,500 a time. About 1,200 animals have died in quarantine kennels in the past 10 years.
Alex Ross of the RSPCA said: "We were very encouraged by the meeting with Mr Brown. All the indications are that the Government is keen to get on and change the law."