But the fraud was discovered when benefits staff noticed the same address was being used for multiple claims, Snaresbrook Crown Court heard.
Thomas, an illegal immigrant, was jailed for seven years while Abiola, also a Nigerian national with leave to remain in the UK, received two-and-a-half years.
Passing sentence, Judge William Kennedy said: ‘This was no less than a criminal industry, with simple and eye watering criminality designed to maximise the loss to the public.‘ It was a difficult investigation carried out with skill and tenacity.
‘The largest single joint conspiracy [of its kind] for these departments and the actual loss was kept down because of the work of both departments.’
Judge Kennedy also indicated that both Thomas and Abiola should be deported at the end of their prison terms.
The pair, who carried out the scam between January 3, 2007 and October 7, 2011, tried to claim £827,000 from HMRC, securing £43,000.
They also claimed £3 million from the Department of Work and Pensions and received £44,000.
With Abiola’s help, Thomas used stolen personal details to complete 2,495 handwritten application forms, which were sent to the appropriate departments for processing.
It is believed that others unknown to investigators, also provided postal addresses and assisted with correspondence.
When the claims were successful, the pair withdrew cash from acquaintances' bank accounts or from bogus post office accounts that Thomas, who masterminded the scam, had set up.
As well as analysing tax credit records, computer systems, hand written application forms and bank account details and listening to hours of recorded phones calls to the Tax Credit Helpline, HMRC investigators viewed CCTV footage showing activity outside various North London Post Office ATMs and carried out surveillance on Thomas.
He was arrested outside a cash point at Upper Clacton Post Office in Hackney, east London last October 7 where he was found to be in possession of 17 Post Office accounts.
He also had two mobile phones and two fraudulently completed application forms addressed to Job Centre Plus.
Abiola, a mother-of-one, was caught on the same day with £4,125 cash in her handbag, which she claimed was child benefit payment.
Thomas, of Hackney, east London, admitted three counts of conspiracy to defraud and money laundering.
Abiola, of the same address was found guilty of four counts of conspiracy to defraud, money laundering and possession of criminal property following a trial at the court in August.