Labour's newly appointed shadow health secretary has said she will consider whether to join party leader Jeremy Corbyn and shadow chancellor John McDonnell in supporting the provision of homeopathic treatment on the NHS.

"I know lots of people who know about benefits of homeopathy," Heidi Alexander told BuzzFeed News. "Whether it's the right use of public money is another thing altogether. I'm open to hearing the argument as to why people may think it appropriate."

She added: "I must admit I'm not totally convinced at the moment but I'll have to look at it. I know my own parents are great believers in homeopathy. It's not something that I would immediately support but I'm going to have to look at a whole range of issues. It's not something that I have given hours of consideration to."

Homeopathic treatments, which consist almost entirely of water, are considered to be little more than placebos by many scientists. Jeremy Corbyn has previously signed parliamentary motions and tweeted his backing for homeopathic treatment, while shadow chancellor John McDonnell has held events in parliament for homeopathic practitioners and pledged to protect the "right of access to homeopathy" on the NHS.

A Labour party spokesperson said they were unaware whether Corbyn would back homeopathy on the NHS as party policy.

Alexander, the MP for Lewisham East, made her name with the successful campaign to save her local hospital's A&E department, which was at risk of being closed down by the coalition government. She admitted she had been surprised to be offered the job of shadow health secretary by Corbyn since she is not "from exactly the same part of the political party as Jeremy" and had nominated Andy Burnham to be leader.

"I got a phone call at about 7:30 [on Sunday evening]," she explained. "It came as a bolt out of the blue, to be honest. I certainly didn't anticipate being offered the job of shadow health secretary. Jeremy spoke to me personally. We spoke briefly and I decided it was the right thing to do for the party to accept the job."

When asked whether Corbyn could be elected prime minister in 2020 she said: "Yes. There's a lot of water to go under the bridge between now and then but I told Jeremy yesterday he has my respect and support. Anyone who stands to be leader of the Labour party has that. That isn't to say there won't be some difficult and important debates in the years ahead, but I want to be around the shadow cabinet table to take part."

Alexander said she would campaign against some aspects of the Transatlantic Trade and Investment Partnership (TTIP) between the EU and the US, which has become a bone of contention among many of Corbyn's supporters for fear it could lead to the privatisation of parts of the health service: "TTIP is something a lot of people are rightly concerned about. The NHS should be exempt."

But she said it would be wrong to dismiss the free trade agreement altogether: "There are some potential economic benefits associated with TTIP and you can't throw the baby out with the bathwater. What we don't want is our public services opened up to constant legal challenges by corporations."

Alexander, who said she wanted to campaign on quality of care for elderly people and mental health provision for the young, said she was not concerned that Corbyn's top shadow cabinet positions went to men: "I think if you look at the cabinet across the board it's over half women. I'm not sure it should be about what particular position each person holds."

She also said she did not necessarily support all of Corbyn's policies – "It's very unusual to find someone you agree with 100% of the time" – but insisted that all wings of the party needed to work together in order to make his leadership a success.

"We don't know at the moment what votes will be coming before us over the next few months and years. Jeremy has been very clear that he wants a new kind of politics: one that is open and inclusive. I'm not saying it's all going to be plain sailing. It's important the party stays together."