At a meeting of immigrants in Tel Aviv last week, Sharansky rehearsed their grievances over jobs and housing. But the heart of his message was that "Russian immigrants want to become Israelis, without leaving their culture at the airport".
Sharansky, 47, his small form bouncing with energy nine years after he was freed in a prisoner exchange in Berlin in 1986, is the catalyst for what is likely to become a new party and the one figure who might make it work. Labour won the last Israeli election in 1992 by taking more than half the Russian immigrant vote. But recent polls suggest that the Russians - as they invariably remain known in Israel - are now disillusioned and 45 per cent say they would vote for a new immigrant party.
It is not difficult to see why they are upset. They are a highly educated group - more than 60 per cent have college degrees compared to 25 per cent of Israelis - and there was no way, for example, that Israel could find the 13,000 immigrants who had worked in the arts the same jobs as they had held in the old Soviet Union. The same is true of the 61,000 engineers, often with specialities such as railway and bridge building, not much needed in Israel.
Helen Sholk's experience is typical. She arrived with her husband, Igor, from St Petersburg in 1990. Both had skills which were peculiarly difficult to transfer: he was an art historian specialising in Rubens and she was trained for the theatre. Arriving in Jerusalem with $500, he went to work on a construction site and she became a hotel maid. They started a theatre project but it foundered. Then Igor found a job in a shop, says Helen: "It was a good salary and he liked it but he sprained his back lifting a box and he has not worked in a year."
But for the great majority of immigrants, well ahead of economic motives or to escape anti-semitism, it is for the good of their children that they came to Israel and the experiences of Helen's sons at school, being called "dirty Russians", proved the final straw. She is returning to St Petersburg at the end of June to live with her parents and look for a job.
Other Israelis are often irritated by the complaints of Russian immigrants. Ministry of Absorption spokesman Amnon Beeri says that some 30 per cent of the Russians are working in their original professions while another 40 per cent are in related professions although at a lower status: "An X-ray doctor might be an X-ray technician."
Among Israelis facing competition from the Russians, irritation is replaced by real anger and often racist stereotypes. "Crime, prostitutes, alcoholism - that is what the olim (immigrants) have brought to Beersheva," said one local councillor. Tsvi Na'im, a councillor from Afula in northern Israel, said: "Russian women are just prostitutes, causing divorces and not serving in the army." And Labour and Social Affairs Minister Ora Namir seriously damaged his party's standing among the immigrants by saying last year that it was just the elderly and sick who were coming to Israel.
Immigrants quote police statistics showing that Russians are less likely to commit crime than other Israelis. Some members of the "Russian mafia" do live in Tel Aviv, and Israeli banks are used extensively for money laundering, but there is little sign of the mob operating here. Russian prostitutes usually stay for four or five months, then go home.
Will the anger of immigrants produce political action? In 1992 a small immigrant party called Da stood in the election and got nowhere. Russians then felt the ruling right-wing Likud had done nothing for them and 54 per cent voted for Labour, giving the party a crucial edge. Current polls show that two-thirds of the immigrants now favour Likud and right-wing parties.
Sharansky wants any new party to have a broader ideology than bread-and- butter issues. He told last week's meeting in Tel Aviv: "In the nine years since I came to Israel the government has only tried to solve the problems of the state and not of society." His aim is to create something more pluralistic. In his last column in the fortnightly Jerusalem Report, he attacks the Zionist idea of the new Jew which "meant rejecting the culture that each successive wave of immigrants brought with it".
Culture here means more than Russian libraries, theatre, films and television. A major point of friction between the incoming immigrants and Israelis is that the Russians are profoundly secular and they are entering a Jewish state where marriage and burial are handled entirely by the Rabbinate. Helen Sholk says that one of the reasons her family was unhappy is that her husband is Jewish but she is not - in Judaism the woman's faith is especially important. The Ministry of Absorption says 13-15 per cent of immigrants are not Jewish according to the Rabbinate, so this is a common problem. A political colleague of Sharansky, Eli Kashdani, says that a Russian immigrant "who gets killed in battle in the Israeli army might not be able to get buried".
By the end of the century one in six Israelis will have come from the former Soviet Union and their impact is bound to be profound.
Some may be hesitating in Moscow or St Petersburg, deterred by others' experiences, but thousands more are coming from Ukraine and Central Asia.
"We are not like a transfusion of new blood into Israeli society," said a doctor at the Tel Aviv conference. "Russian immigration is more like the transplant of a new organ which may be accepted or rejected by the patient."