One of the Conservatives’ most generous donors has criticised the party’s reliance on wealthy benefactors, and has urged the party’s chief executive, Mick Davis, to be “more energetic” and seek £50 gifts from ordinary members.

John Griffin, the taxi entrepreneur who has given £4m to the Tories over the last six years, said he had put an alternative fundraising strategy to senior party officials including Davis to seek smaller gifts but his ideas had not been taken up.

Tensions between Griffin, the founder of Addison Lee, and Davis, the mining executive who is also the party’s treasurer, can be disclosed days after a number of wealthy donors failed to attend the party’s annual Black and White ball.

Some of the party’s biggest donors are withholding payments because of concerns over Theresa May’s leadership, the lack of a policy agenda and paralysis over Brexit.

Griffin, who is the party’s second most generous donor since 2013, told the Guardian the Conservatives must become a mass party that is funded by signed-up members.

“As one of the people who have given big amounts, I want more people to join me and give smaller amounts. We wouldn’t be asking them for £1m, we would be asking them for £50,” he said.

He said he had suggested sweeping changes to party funding to May two years ago and more recently in a meeting with Davis, but had been frustrated by the lack of progress. Davis is the party’s most generous donor over the last six years and is the former chief executive of the mining firm Xstrata,

“I spoke to Mick about changing the funding model. What he should have done was bring me forward into the office and look at the detail of it. Mick Davis should get more energetic around taking onboard the task,” he said.

Griffin, 76, said he had told party officials he had given large amounts in the past but did not feel it was right for a wealthy few to support the party in the future.

“They [party officials] asked me how I felt about it [giving large amounts] and I said ‘not great’. If I can say that, there are a lot of people out there who would be generous donors who think the same. Asking for a contribution while everyone else is doing something, it might be healthier,” he said.

According to the Electoral Commission website, the Conservative party has received £147m in donations since 2013, excluding public funds. Almost 30% of this (£42.8m) came from 20 individual donors.

Davis, 60, was appointed chief executive of the party in 2017. Conservativehome website has claimed he has spent much of his time placating unhappy donors.

Griffin, who stood down from Addison Lee five years ago, said the problem of had has been exacerbated by the Brexit stalemate but said he would consider contributing towards a general election campaign.

“We are heading towards being the laughing stock of Europe anyway so we may as well go the whole hog and call another election,” he said.

Griffin’s comments came after ministers and donors gathered last week for the party’s annual fundraising Black & White ball in Battersea, south London.

The event has been criticised for selling access to ministers, with one anonymous donor paying £75,000 for a private night at the Proms with May.

Reports have claimed that many other big donors stayed away. Griffin was in Dubai on that night.

Party officials would like to copy Labour’s successes in bringing in cash from hundreds of thousands of members instead of relying on monied donors from the world of business and finance.

Figures released in August showed Labour raised nearly £56m in 2017 while the Tories managed £45.9m.

Legacies from dead Conservative donors were double subscription fees in 2017, with just under £1.7m paid in legacies versus £835,000 from memberships.

The Guardian interviewed three other Tory donors who have given more than £500,000 since 2010. All said they were unsure whether to give cash to the party at present. One said the party “appears to be dying on its feet” while another said he wanted to see who was going to lead it into the next election before committing any cash.

However another peer, Lord Fink, a former party treasurer under David Cameron, said he was not aware of any fundraising problems and voiced support for Davis.

“Mick is doing a fabulous job for the party,” he said.

The Tories have traditionally concentrated their fundraising efforts on the Leader’s Group, where the party’s richest donors pay £50,000 to dine with the prime minister, and the Black and White Ball.

The Guardian disclosed that May had dinner with the co-chair of the controversial Presidents Club only weeks after she had criticised the charity’s event at which female staff were allegedly propositioned for sex.

Bruce Ritchie donated at least £50,000 to the Conservatives’ Leader’s Group (CLG). He was one of 48 benefactors who socialised with the prime minister between 1 April and 30 June last year, with others including business people who support a hard Brexit and oil executives. In total, donations to the CLG amounted to £2.4m.

The Tories were forced on Sunday night to change the description of a donors’ club after being accused of selling access to the chancellor, Phillip Hammond.

Individuals were being offered membership of a “chancellor’s group” that the party said had the “overt patronage of the chancellor” and offered the chance to “discuss topical issues” with key finance ministers, go to post-budget briefings and get “monthly updates on the economy”.

The Conservative party has been approached for a response.

The Conservatives’ biggest individual donors since January 2013:

1 Mick Davis, former CEO of Anglo-Swiss mining giant Xstrata PLC - £4,470,119

2 John Griffin, founder of Addison Lee – £4,005,300

3 Lord Michael Farmer, hedge fund founder and former metal trader – £3,509,854

4 Lord James Lupton, former deputy chair of Barings Bank – £3,126,411

5 Lord Alexander Fraser, former head of Barings Securities – £2,597,400

Source: Electoral Commission. Figures do not include unincorporated associations or firms.