The issue was also mentioned in the Queen’s Speech on Wednesday.
Johnson’s article for the Telegraph, published on Wednesday, was in response to a letter Abta sent him.
Johnson wrote: “Let me give you an example of an injustice that is unfairly affecting millions of families across this country. Back in March I got a letter from the head of the Association of British Travel Agents. It made my eyes almost start from their sockets.
“It seemed that in the past few years there had arisen a rampant culture of claiming insurance at the end of the holiday: not for theft, or for loss of valuables – but for an upset stomach... We have all at some time been laid low by a dodgy prawn; but these numbers seemed outlandish."
Tanzer said in a blog on the Abta website: “As we have made clear over the past few months this issue is one that must be tackled urgently.
“The government’s proposals are a step in the right direction for addressing Britain’s compensation culture.
“However, they are not enough in themselves. More urgently for the travel industry, we need the government to address the fixed costs regime and we will continue to make this point to ministers and MPs both privately and through our campaign, which has received widespread national media coverage.
“It is extremely positive that this issue now has the attention of decision-makers at the highest levels of government.
“We will continue to engage with the foreign secretary, Boris Johnson MP, and the new Justice Secretary, David Lidington MP over the coming weeks.”
He added: “Elsewhere the Queen’s Speech was slimmed-down and likely reflects the difficulty the government is anticipating in passing some legislation through Parliament without a majority.”