A significant number of ministers in Boris Johnson’s new government have been either hostile to or ambivalent about abortion and gay rights, according to their voting records.

The new prime minister has hailed his “cabinet for modern Britain”, but five of them opposed the introduction of same-sex marriage in England and Wales during a final House of Commons vote in 2013.

They included the culture secretary, Nicky Morgan, who has since said she would vote in favour of gay marriage if she was given the chance again, the defence secretary, Ben Wallace, the justice secretary, Robert Buckland, and the home secretary, Priti Patel.

The fifth minister to vote against marriage equality is the new education secretary, Gavin Williamson, whose in-tray will include how to respond to campaigns objecting to primary schools teaching about same-sex relationships. A sixth cabinet minister, the Welsh secretary, Alun Cairns, opposed the marriage (same sex couples) bill on its second reading but was absent for the final vote.

Sixteen of the 22 MPs in the cabinet were absent earlier this month when the House of Commons voted to allow same-sex marriage in Northern Ireland.

Johnson himself was absent for the vote and for another on the same night to liberalise access to abortion rights in Northern Ireland. Fifteen of the cabinet were absent from the latter vote while the new foreign secretary, Dominic Raab, voted against.

Just two were present in the House of Commons chamber in March 2017 to vote in favour of a bill that decriminalised abortion for the first time by repealing a law that dated back to Victorian times. It was opposed by Wallace, while 18 MPs who are now in the cabinet were absent.

On another so-called issue of conscience, only Robert Jenrick, the new housing secretary, voted in favour of a bill that proposed to change the law to allow doctors to help terminally ill people end their lives. It was overwhelmingly rejected by MPs on the day, while nine members of the current cabinet were absent.

Elsewhere on policy issues that have split the Conservatives and other parties, there was overwhelming support among members of the current cabinet for the third runway at Heathrow.

Twenty voted last June in favour of expansion while just one, Theresa Villiers, was opposed. Despite having pledged to “lie down in front of the bulldozers” to stop a third runway, Johnson was the only member of the current cabinet who was absent for the vote. The then foreign secretary was criticised for travelling to Afghanistan at the time.

On other environmental fronts, the past votes of most cabinet members are likely to leave their green credentials in some doubt. Eighteen voted against an attempt to ban fracking while 19 voted for a climate change levy to be applied to electricity generated from renewables.

While the cabinet is heavily weighed towards trenchant supporters of Brexit, there are some nuances in terms of how their votes have split during key moments of the past year.

When the first indicative vote was put before parliament on whether to accept a no-deal Brexit, six voted for the option. They were Johnson, Raab, Patel, Jenrick, Wallace and Grant Shapps, now the transport secretary.

They now sit around a cabinet table with those who opposed the option: Buckland, the Scotland secretary, Alister Jack, Morgan and Alok Sharma, the international development secretary. Others, as part of the previous cabinet, abstained.

On Theresa May’s ill-fated Brexit deal, just five of the 22 MPs in the new cabinet voted against it in the first and second so-called meaningful votes. They were Johnson, Patel, Raab, Shapps and Villiers.

As Tory ranks closed during the third vote on 29 March, just two of the 22 opposed it: Patel and Villiers.