British authorities are now convinced that the assassin who killed Said Hammami, the Palestine Liberation Organization representative here, was an amateur zealot acting on his own.

Agents investigating yesterday's killing, it was learned today, have all but ruled out the possibility that the killer was a professional hit man employed by a hardline Arab state or Palestinian faction.

PLO sources told reporters in Beirut that the PLO is sending three officials to London to investigate the slaying. The PLO issued a statement in Beirut that blamed the killing on "Zionist and imperialist assassins," vowed revenge and said the organization would "hold Britian responsible" until the killer is caught.

A man identifying himself as a spokesman for the Voice of the Palestinian Revolution called United Press International in London and said Hammami had been shot "because he made contact with the Jewish country." Palestinian officials here and in Beirut said they had never heard of such an organization.

Hammami, 35, was gunned down in his Mayfair office by man described as of Middle Eastern origin. The killer fired three shots into his victim and then was surprised by a group of students who heard the firing. He shoved them aside and escaped into the throngs on nearby Oxford Street.

Hammami, spokesman here for Yasser Arafat since 1971, had a reputation as a "moderate." This was based on statements he made and later retracted that suggested the state of Israel might survive alongv fe a Palestinian state.

His wobbly position on Israel's future had been led the press here to theorize that Hammami was executed on orders from Libya, Iraq or more extreme Palestinian Arab groupings.

But the British investigators reject this on several grounds. For one thing, Hammami had Arafat's confidence and even the harshest Arab groupings are believed to be reluctant to engage in war with the PLO leader.

For another, a hardline state presumably would have employed a professional team of killers and Hammami's killer was anything but. The three unprofessional mistakes he made, authorities say were these:

He acted alone, failing to protect his escape; he used a gun, which makes noise, instead of a knife and he failed to clear his line of retreat.

Meanwhile investigators are now all but satisfied that the Syrian medical attache and his driver who were blown up in their car on New Year's Eve were victims of their own bomb. The pair, it is believed, intended to plant their device outside an Egyptian travel office when it went off in their hands.

The authorities think they were acting more or less on their own, trying to protest presidentAnwar Sadat's peache initiative.

In other unexplained killings in the Middle East recently, Daivd Holden, chief foreign correspondent for the London Sunday Times, was slain near Cairo and two Arab officials in the occupied West Bank were assassinated.