The findings were uncovered in L&C's Stamp Duty report, which investigated how many homes across England are and will be available for £500,000 or less in the next 10 years.
This follows the government's announcement in the 2017 Autumn Budget that first-time buyers will pay zero stamp duty on the first £300,000 of any home that costs up to £500,000.
The report looked at the potential increase in house prices over the next decade, using past L&C data on future first-time buyer deposits, and identified which cities are likely to benefit from the stamp duty cut in the future.
The mortgage broker found that in 10 years time, 51 per cent of the 52,002 London properties that currently qualify for a stamp duty cut for a first-time buyer will not benefit.
David Hollingworth, associate director of communications at L&C, called for the end of stamp duty for first-time buyers.
He said: "Abolishing stamp duty for first-time buyers altogether would help all those looking to get on the ladder, with one less expense to worry about.
"Our research shows that many of the first-time buyers, especially those based in southern England, who are set to pay less or nothing will need to act fast before many of the properties currently eligible fall out of the price bracket that qualifies for the cut."
The 15-page report found that 21 per cent of first-time buyers will change the area in which they want to buy to avoid stamp duty.
This figure rose to 37 per cent in London.
On the other hand, only 11 per cent of those in the south west have changed the area they want to move to in light of the recent changes.
The analysis found that 53 per cent said they felt that it is unfair that some areas in England will receive a greater discount than others as a result of the stamp duty changes.
Interestingly, the report also found that 31 per cent of first-time buyers do not know if the stamp duty abolition will benefit them when they buy their first home.
A massive 65 per cent of English first-time buyers know a little about the stamp duty changes introduced at the end of 2017, but only 18 per cent know a lot or a reasonable amount.
Worryingly, 18 to 24-year-olds are less likely to have any knowledge of the stamp duty changes – which affects 51 per cent of first-time buyers.
