The senior Conservative told undercover reporters from the Telegraph and Channel 4's Dispatches, to be broadcast today, he would submit questions to ministers on behalf of a paying client, without revealing their identity.
Rifkind also described himself as "self-employed" and had to "earn my income" - despite being paid 67,000 by the taxpayer for his work as an MP. The disclosure that two of Britain's most senior politicians are embroiled in a new "cash for access" scandal highlights Parliament's failure to address the issue which has plagued British politics for a generation.
Sir Alistair Graham, the former chairman of the Westminster standards watchdog, said it was "shocking" that two experienced MPs responded to the approaches in the way they did.
He expressed concern that Rifkind was "so willing to sell himself" with his "enormous range of contact lists". He added that it was against the rules for Straw to attempt to negotiate a business contract in his Commons office.
More than five years ago, Prime Minister David Cameron warned that lobbying was the "next big scandal" and promised to tighten the rules - a pledge which has not been properly enacted. Over the past few months, reporters approached 12 MPs asking if they would be interested in joining the advisory board of a Chinese company.
They were chosen because of concerns about their business activities. Six did not respond and one said his contacts were not "for sale". Straw and Rifkind agreed to enter talks with the fictitious Chinese company looking to expand its business interests in Europe.
Last year Rifkind registered earnings of 69,610 - more than 1600 an hour - from his work outside of Parliament, while Straw earned 112,777 from his outside business activities.
Analysis of MPs' earnings showed they made more than 7.4 million from outside work in the past year.
Undercover reporters met Rifkind at the fictional Chinese company's Mayfair office last month.
Rifkind, who served as Foreign Secretary under Sir John Major, said he could meet "any ambassador that I wish to see" in London.
In a second meeting, he suggested he would be willing to write to ministers on behalf of the company without declaring the name of the firm.
Graham said it would be a "clear breach of the code of conduct if he's not explaining he's acting as a consultant on behalf of a particular company when he's seeking information".
The undercover reporters met Straw at his House of Commons office.
The MP said he had helped ED&F Man, a commodities firm with a sugar refinery in Ukraine, change an EU regulation by meeting officials in Brussels.
He also said he had overturned a law in Ukraine that would have hindered the commodities firm operating a factory they had recently upgraded.
The law made their activities "completely uneconomic" and so Straw took company representatives to see Mykola Azarov, the then Ukrainian Prime Minister, in September 2011. "It's a combination of sort of charm and menace ... he [the Prime Minister] understood."
Yesterday it was reported that Straw will refer himself to the Parliamentary Commissioner.
Straw and Rifkind denied wrongdoing. A Straw spokesman said: "He has always conducted himself ... in accordance with the appropriate rules."
He said there was "nothing inappropriate" in him using the "knowledge and experience" he has acquired as an MP after he stands down.
Asked about Straw's boast that he operated "under the radar", his spokesman said: "This was a reference to his preferred strategy of effecting a change to regulations by discussion and negotiation, rather than conducting a high-profile public campaign."
Straw said that when he mentioned the 5000 fee he gave it as an example and not as part of a negotiation.
Rifkind said he believed the "firm" had sought his help as a former Foreign Secretary rather than as an MP. He said: "I have never undertaken, nor would I undertake, any lobbying as an MP on behalf of any private organisation from which I was receiving remuneration."
Dirty politics UK style
It was an issue British Prime Minister David Cameron promised to tackle head-on after predicting it was "the next big scandal waiting to happen".
But five years on from his warning about the problem of lobbying, concerns about "the far-too-cosy relationship between politics, government, business and money" persist in Westminster.
Since taking office Cameron has increased the period in which ministers cannot lobby the Government after leaving office, from 12 months to two years.
The coalition also brought in legislation to introduce a register of consultant lobbyists. However, the register has yet to be implemented.
MPs are bound by a code that includes specific rules about lobbying and outside interests as well as "general principles" by which they should abide, including selflessness, integrity and honesty.
MPs should ensure official resources are used only "in support of their parliamentary duties". The Commons members' handbook adds that offices should not be used for "private business activity".
The code states MPs must always "declare a relevant interest" when dealing with ministers and public officials.
