Reuters / Daniel Munoz
The analysis of HMRC figures found that the government lost £31.6 billion of tax revenue due to a black market in products like spirits, beer, and cigarettes.
Between 2010 and 2015, £13.9 billion in tax was lost due to the black market in cigarettes, £5.8 billion was lost through the black market in spirits, £4.8 billion was lost due to the illicit trade in diesel, and a further £3.5 billion ($4.4 billion) to wine.
The TPA says that high taxes on such products simply promote the illicit markets, and that reducing rates on such products would dramatically increase tax revenue for the government.
It says that closing the "tax gap" - the difference between the amount due and the amount actually collected - would be enough to fund a 1.5p cut in the basic rate of Income Tax, which is currently 20% for those who earn up to £31,785.
The calls for a reduction come in the run-up to Chancellor Philip Hammond's Autumn Statement on November 23.
The Autumn Statement is one of the two most important speeches the UK chancellor makes every year, the other being the Budget. Hammond will use it to lay out his taxation and spending plans, based on economic predictions made by an independent group.
The news comes as experts warned that Hammond faces a £25 billion ($31 billion) "black hole" in the government's finances as he prepares the statement. The International Monetary Fund warned at the beginning of November that a Brexit-induced economic slowdown would result in lower tax receipts for the government.
The TPA report says: "HMRC has clearly been unsuccessful at claiming these duties for some time and therefore it needs to take decisive action, not introduce policies that make it worse. It is unfair that higher taxes for ordinary families are often used to make up the shortfall."
"The loss of £31.8 billion in revenue over a five year period could have funded a 1.5p cut in the basic rate of Income Tax. Not only would this have helped millions of ordinary families, but it would also have had a big impact on the jobs market, which is particularly important at this time."
John O'Connell, chief executive of TPA, said: "Our ludicrously complicated, punitive tax system not only hits hard-pressed families with crippling bills but also affects frontline services by depriving Treasury of revenue lost to the black market, all the while lining the pockets of those peddling dodgy tobacco, alcohol and diesel."