Biggs himself is unlikely to be shipped home as a result of the agreement, since Brazilian law does not allow the prosecution of crimes committed more than 20 years ago. The train robber has consulted a British expert on extradition law, Alun Jones QC, and years of legal wrangling in the Brazilian courts could be in prospect.
Even if that fails, Biggs could cross to neighbouring Venezuela, which still has no extradition treaty with Britain, or go slightly further afield to Costa Rica, which has an equable climate, is unusually peaceful and democratic by central American standards and has harboured leading American fugitives, such as the financier Robert Vesco, in the past.
Contrary to its image as the destination of choice for those feeling misunderstood by the law, however, Latin America has few other places of refuge. There may be anarchy in Haiti and Colombia, but they have extradition treaties with Britain, though enforcing them is often difficult. The addition of Brazil brings the number of Britain's extradition partners to 107, including 30 countries which have signed the European Convention on Extradition. Russia is among another five in the process of ratification, which means there is almost nowhere to run to west of the Urals. We even have an extradition deal with San Marino.
Clare Montgomery QC, another specialist in the field, said the number of extraditions from other countries sought by Britain each year had risen from "low double figures" in the 1960s to about 150. The figures were roughly the same in the other direction. "The increase is due to the larger number of extradition treaties we have, as well as wider agreements such as the European Convention," she said. "There is also much more international crime."
Reciprocal arrangements with 47 Commonwealth countries eliminates much of the rest of the world as a hiding place, although there are significant omissions, such as Pakistan. The Home Office will not comment on countries which are not extradition partners, or where it is seeking to negotiate agreements, but a list of nations which have signed treaties with Britain shows that the fugitive has most choice in Africa. Liberia is the only non-Commonwealth country on the continent to have come to an agreement, leaving plenty of scope, from Morocco - probably the closest point of refuge to these islands - to Egypt and Namibia. South Africa was once a tempting bolthole, but jurisdictional difficulties with Britain have eased since the end of apartheid.
If you can't stand the heat, there are few places to go. Belarus and Ukraine have yet to reach extradition agreements with us, but the winters are as appalling as their economies, and they are unlikely to be willing to jeopardise their future European credentials.
Leaving out the central Asian republics and other similarly unappealing corners of the world, the most promising region for the involuntary expatriate is east Asia. Although Thailand is out, one can escape to China, Vietnam, South Korea and - perhaps most surprisingly - Japan.
The favourite, however, must be the Philippines. As the late Lord Moynihan knew when he went there to avoid his gambling debts, the pound goes a long way and English is widely spoken. He opened a chain of massage parlours and left behind a couple of half-Filipino sons who unsuccessfully tried to claim his title.
The countries to avoid are those which have agreed to carry out British arrest warrants, although these include Ireland, which has several times found technical flaws in warrants for IRA suspects. It is not enough, however, to flee somewhere which has no formal agreements with London: if the government is sufficiently autocratic and your presence sufficiently inconvenient, you may be deported without legal niceties.
This applies even to northern Cyprus, which Britain refuses to recognise as a country at all. It has attracted the likes of Asil Nadir, founder of the collapsed Polly Peck empire, and, it is believed, Kenneth Noye, a career criminal who helped to launder the proceeds of the Brinks-Mat robbery and is now sought for questioning in connection with last year's "road rage" killing of 21-year-old Stephen Cameron on an M25 slip-road.
"The northern Cypriot authorities do co-operate loosely with their British counterparts when it suits them," said Ms Montgomery. "People have been deported unofficially into the arms of the British police." If you have to leave in a hurry, it seems, better make for Manila or San Jose (capital of Costa Rica, as you may need to know).