Now the Home Office has accepted that the Balogs were not bogus after all but were genuinely fleeing racial persecution after being the victims of at least eight attacks by skinhead gangs in the Slovak Republic.
Their successful application for asylum is, with three other favourable verdicts for Slovak "Roma" families, to be used by lawyers as a test case for hundreds of similar asylum claims.
The issue is potentially embarrassing for ministers who denounced the gypsies as "economic migrants".
Jack Straw, the Home Secretary, told radio listeners in January: "Not ... one of these has been found by the independent tribunals to have had a well-founded claim for asylum." He accused solicitors of helping gypsies to "manufacture, invent [and] pursue" claims.
But a special adjudicator at the Immigration Appellate Authority has ruled in favour of eight Czech and Slovak gypsies who had claimed they were being persecuted. The Home Office, which earlier described the cases as "manifestly unfounded", has decided not to appeal against the decisions.
As critics of the gypsies will have suspected, Mr Balog, 28, has never done a full day's work in his life.
On the only occasion he was offered a position - at a Slovakian brewery - he was forced to leave on his first day after colleagues refused to work with a gypsy.
Other firms refused even to consider someone of his racial background and his job centre openly admitted there was no point in him coming in.
Instead he was forced to root around in rubbish dumps for bottles, paper and iron to sell.
Apart from the physical attacks, one of which left youngest daughter Valeria unable to speak for weeks afterwards, the family was constantly taunted with shouts of "Go Back to India". The Roma are described by other Slovakians as "blacks" and refer to themselves as such, despite their skin colour.
When Mariana, 27, was expecting elder daughter Marika, now five, she was told by her local hospital that they did not accept Roma. After protesting she was allowed to have her baby in a side room housing the building's heating controls.
By last year the family were unable to afford their rent and were moved into an out-of-town housing scheme reserved for gypsies. In August, they fled to Britain on a bus. Immigration officials considered their case for asylum and rejected it in November.
But the family, who are living in a two-bedroomed first-floor flat in Muswell Hill, north London, this month won their appeal.
Although none of the family speaks English, Mr Balog said he would accept any kind of work, while his wife is seeking employment as a seamstress. Marika has already started attending a local school.
The family has some contact with the other Roma families, although many are housed in Kent after arriving at Dover. The gypsies organised a dance evening at Swiss Cottage, north London, last weekend.
Through an interpreter, Mr Balog said: "No one should have to live through what we have lived through. The Home Office don't seem to have any idea what is going on in our country."
He is grateful to the British public. "People are so polite. If we go shopping people help us; in Slovakia we are not even allowed into many of the shops."
Deri Hughes-Roberts, of the Refugee Legal Centre, said the verdicts would be test cases for the 370 Roma still appealing for asylum in Britain. Another 523 Czech and Slovak refugees have already been removed from Britain.
Mr Hughes-Roberts said: "If the Home Office chooses to ignore the decisions in the test cases, we will be arguing before special adjudicators that the decision has to be treated as being extremely persuasive and that they should allow the outstanding appeals."
A Home Office spokesman said the fact that eight appellants had been successful showed that the adjudications were fair and independent.
He pointed out that since the beginning of December, 24 Slovaks and 12 Czechs have had asylum appeals dismissed.
"Each case will continue to be considered on its individual merits, in the light of all available information about the treatment of Roma in the applicant's country of origin. If asylum is justified this will be granted," he said.Reuse content