A tennis match involving David Cameron and Boris Johnson in return for a £160,000 donation to the Conservatives will go ahead, the justice minister, Chris Grayling, has said.

Challenged on BBC Radio 4's Today programme over the Tories' reliance on City donors and oligarchs, Grayling rejected the criticisms, saying that his party's donors would not influence policy.

He defended the £160,000 donation to the Conservatives from the wife of a former member of Vladimir Putin's government, which she has paid to play tennis with the prime minister. Grayling said the payment from Lubov Chernukhin was "entirely legitimate".

The prime minister has insisted that Vladimir Chernukhin, who served as deputy finance minister in Putin's first administration, is not a crony of the Russian president and it would be "the wrong thing" to give the money back.

Asked whether Cameron's tennis match was going ahead, Grayling said: "Well, the tennis match is going ahead because it's a donation from a British woman, a British citizen who is perfectly entitled to make a donation."

Earlier when questioned about the same donation, Grayling said: "The first thing is that a wide range of people contribute money to the Conservative party. They have to be legal British donors and in that particular case this was a British woman who happens to be married to a former Russian minister who was sacked by Vladimir Putin 10 years ago, but we don't tend to say to people you can't give money yourself because of your husband's role in life.

"But also when you contribute money to the Conservative party, you don't buy policy decisions. Those people who contribute money to the Conservative party … do it because they believe a Conservative government is best for Britain."

Told it was ludicrous to make that remark as major donors to the Tories thought they would get a policy return, Grayling replied: "This is an argument that's been used for years by the Labour party and it's not true now and it was never true."

He added: "The truth is, it doesn't happen. Donors of the Conservative party don't buy policy, they contribute towards a belief that a Conservative government is best for Britain. I am afraid in the case of the Labour party there's a very clear link – what Len McCluskey of Unite asks this week, next week will become Labour policy."

Michael Dugher, the shadow Cabinet Office minister, said Grayling's claims were "absolute garbage".

He said: "Chris Grayling seems to have confused the Labour party, who never have and never will link donations to policy, with the Conservative party, who have rewarded the few City fat cats who give them millions of pounds with tax cuts for millionaires and hedge funds.

"Unlike the Tories, who rely on dodgy dinners and huge donations from hedge funds, the largest section of Labour's funding comes from our members, a fact we're proud of. Rather than wasting people's time with these pathetic smears, the Tories should be getting their own house in order."