A Cabinet minister has defended the peerages system in the UK as she said those in the House of Lords had “usually done enormously good work”.

A Sunday Times report showed 15 of the last 16 Conservative Party treasurers have been offered a seat in the Lords, having each donated more than £3 million to the party.

But International Trade Secretary Anne-Marie Trevelyan said it was key to have a “rich mix” in the upper chamber.

The Tories have denied any link between the donations and the nominations to sit in the Lords, in the latest twist in ongoing allegations of sleaze.

On Monday, Ms Trevelyan said “many business people, who have donated to their parties – Lord Sugar is one for the Labour Party, we have some on our side – do so because they believe in political activity”.

She told Sky News: “We have an incredible system in the UK where we don’t ask the state to fund our political parties and if we didn’t have the private donations that come through from donors large and small – in my constituency, people donate £25 a year and donors who can provide more, do more – if we didn’t do that the taxpayer would be funding political activity.

“I think our UK system is uniquely well-placed to ensure that we get this broad stretch … the unions fund a great deal of the Labour Party’s activity, again that’s from many, many small voices, and then some large ones too.

“It’s a mix which brings a real depth of voices to our political parties across the piste.”

Ms Trevelyan insisted there was a formal process in place, but was challenged on ITV’s Good Morning Britain over the Prime Minister’s ability to overrule the Lords appointments commission, as he did with Lord Cruddas.

But she told GMB: “So the Prime Minister always has the final say, the Prime Minister of the day always has the final say, as have other prime ministers in the past.”

Ms Trevelyan told Sky News: “I don’t think that someone who happens to have been an extremely good businessman and has made a great deal of money through business activity – usually also an enormous amount of philanthropy as well, those are the sorts of people who are across our country, amazing people of all political colours – that they should be barred from going to the House of Lords because they have made a lot of money, employed many, many thousands of people, run incredible businesses at their own risk, that that somehow is a bar. That’s not the case.

“Those who choose to put themselves forward in political environments, as well as their business and philanthropic ones, will go through the process just like anyone else, and we want a rich mix in the House of Lords of voices with experience of all the sectors of our country.”