Already furious after vandals desecrated Sands' tombstone and the graves of other hunger strikers in Belfast's Milltown cemetery last week, they said Iranian authorities should stick with a street name "reminding the British government of their oppression and their black history".
"Bobby Sands' sacrifice and that of his nine comrades inspired many people around the world," said Danny Morrison, secretary of the Bobby Sands Trust in Belfast.
"We in the nationalist community, who suffered under British rule, were delighted and proud when Tehran named the street beside the British embassy after Bobby Sands," he said.
Morrison, a former IRA prisoner and friend of Sands, noted that Iran's Islamic government sent a representative to the hunger striker's funeral and presented his mother with a plaque from the Iranian people.
By renaming after Sands' death in 1981 what was formerly Winston Churchill Street next to the British embassy in Tehran, "they were honouring a martyr of the people," Morrison told AFP.
"It is that reminder which annoys the British and which is why they want Bobby's name erased," he said.
"Bobby died not a terrorist, but as an Irish Freedom Fighter. He stood for election in Ireland - which is more than any British minister who rules us has done."
The British Foreign Office dismissed the claims and denied having put pressure on Tehran to change the name of the street.
"There are a lot more important things to talk about between Britain and Iran than the name of a street," a Foreign Office spokeswoman told AFP.
Richard McAuley, spokesman for Gerry Adams, leader of the IRA's political wing Sinn Fein, said Britain's desire to have the street name changed "would suggest to people in Ireland that some aspects of the British approach to Ireland never seem to change".
"The British are obviously embarrassed," another Sinn Fein spokesman told AFP. "It's an attempt to erase the memory of what they have done."
"People across the world remember Bobby Sands as an icon of freedom and struggle, and they recall Margaret Thatcher as an associate of Pinochet, he said, referring to former Chilean dictator Augusto Pinochet.
As for Morrison, he also pointed out that in Belfast, "everywhere you go you are reminded of British imperialism".
"There is Cromwell Avenue, Churchill House, Queen Elizabeth Bridge, the Kings Hall, the Royal Victoria Hospital and dozens of other similar reminders that the oppressors get to write history," he said.
"We recognise that it is up to the people of Tehran to name streets after whoever they choose," he said.
"But we would be very disappointed if they were to give in to the British government - and I appeal to the Iranian authorities not to bow to this pressure but to keep the name of Bobby Sands alive, for he has inspired the spirit of freedom around the world whereas Britain spreads only war and suffering."
Wit and wisdon of Iran: "He was a terrorist. And if the Iranians want to appear serious about fighting terrorism, one place to start is changing the name of that street."
The call comes from a member of Her Majesty's Foreign Office, and the offending road is Bobby Sands Street, a classic example of the wit and wisdom of revolutionary Iran, situated as it is next to the British embassy in Tehran.
Bobby Sands led a dramatic and ultimately fatal hunger strike in 1981 aimed at having him and his fellow Irish Republican Army prisoners jailed for fighting British rule in Northern Ireland classed as political detainees and not common criminals.
"Sixty-six days of no food, and he was dead," as one regular customer at Tehran's Bobby Sands snack bar - another odd Iranian tribute to the IRA man - faithfully recalled. "He was a martyr in the Jihad against the British".
In all, ten men died in one of the most turbulent episodes in the Irish conflict, made all the more traumatic for Downing Street because Sands was also elected to the British parliament before his death.
For Iran, then in the midst of exporting the revolution and celebrating the battle against Western oppressors, Sands' death at the age of 27 struck something of a chord.
Having overthrown the US-backed shah of Iran themselves, the country's clerical leaders immediately felt an affinity with the IRA's armed struggle against occupation and the then hard-line British premier Margaret Thatcher.
Allegations that Iran, along with Libya, was arming the IRA then followed.
But some bright revolutionary spark here also thought what better place to honour Sands than the road behind the British embassy, then called Winston Churchill Street. The great imperialist, after all, was hardly suited for a place on the Islamic republic's new roadmap.
Two decades on, British ties with Iran have improved markedly, while British Prime Minister Tony Blair is pressing on with a peace process in Northern Ireland that has seen IRA prisoners who once served alongside the hunger strikers amnestied.
British diplomats, therefore, say they feel it's time for the street name to be changed, especially in a period where a global war against all things "terrorist" means that such honours no longer even amuse.
During the third of five trips to Iran by Britain's Foreign Secretary Jack Straw over the course of the past two years, Iran's Foreign Minister Kamal Kharazi was politely and discreetly nudged to do the necessary, according to a British Foreign Office official accompanying Straw and Iranian foreign ministry sources.
After all, as one British official once famously pointed out, how would Iran like it if its London embassy address were "Shah Pahlavi Avenue"?
Britain may find the street name embarrassing, but its diplomats are generally extremely cautious not to label Sands a terrorist, given the contentious nature of Irish history.
"There are probably more important things to worry about, and it is not on the top of our list of priorities," asserted Andrew Dunn, a British diplomat and embassy spokesman in Tehran.
All he would acknowledge is that "if asked by the Iranians if we wanted it changed, we would probably reply yes".
Irish republican historians are at pains to point out that Sands was never even convicted of what could be classed as an act of terrorism, even though he was a declared member of the IRA.
Back in 1977, Sands was arrested near the scene of a bombing. At his trial, the judge acknowledged there was no evidence to pin the crime on him and the other three men also arrested, so instead sentenced the group to 14 years' imprisonment each for the possession of just one revolver found in their car.
And pushing the issue too much is also seen as futile, with Iran's Shiite Muslim clerical regime generally not adept at making polite diplomatic gestures to foreign powers.
There is now a precedent - Tehran's municipal council agreed this month to change the name of a street honouring the Islamist assassin of Egyptian president Anwar Sadat, which is a hurdle to the restoration of ties between Cairo and Tehran.
But there is no such pressure to do the same with Bobby Sands Street.
Many Iranians also have something of a soft spot for the hunger striker. For example, Vice President Mohamed Ali Abtahi - a jovial and prominent reformist - once told AFP he felt Sands was a "great man".
Sands, oddly enough, did have a fair bit in common with Shiite Muslims and Persians - a dislike of the English, an extraordinary willingness to embrace "martyrdom" and a passion for poetry.
In light of that, he is one of just a few non-Muslims honoured with a street name here.
Diplomats at the embassy of the Republic of Ireland in Tehran admit the street is something of a tourist attraction for Irish nationals visiting the 25-year-old Islamic republic, saying it drew large crowds during an Ireland-Iran World Cup football qualifier in 2001.
In addition, Irish visitors are sometimes greeted at Tehran airport's passport control with a smile from normally gloomy-faced staff, a raised clenched fist and the statement: "Bobby Sands, no food. Welcome to Iran".
Britain's ongoing irritation over the matter - while far from representing anything close to a diplomatic spat - must nevertheless be leaving Sands grinning in his Belfast grave.
"Of course I can be murdered," the hunger striker scrawled in a toilet paper diary smuggled out of prison before his death. "But I remain what I am, a political POW, and no one, not even the British, can change that."
Two decades on, however, the fight continues.