Sky Atlantic has said it is making a "conscious investment in British drama" ahead of the premiere next week of its first UK-commissioned show, featuring Chloë Sevigny as a transgender hitman.

In the show Sevigny is propelled into taking responsibility for her former partner's brood of unruly kids. Writer Paul Abbott said it combined separate ideas for "two series that shouldn't automatically fit together". But he added: "I get bored with everything looking the same and actually real life slams things against you that aren't comfortable; families that don't fit a jigsaw that all fits together."

The show will air on Sky Atlantic – which largely shows US imports, including HBO's Big Love, in which Sevigny starred – on Tuesday. "I'd love to tell you we had to fight [to get Hit & Miss commissioned] – but I'm so much more pleased that [Sky's] minds were open, because the whole landscape was looking bankrupt of brand new drama," said Abbott, praising the channel's attitude towards commissioning challenging British shows with longer runs.

Sevigny, who had to wear a prosthetic penis to play Mia, a pre-operative transgender assassin, said while she was impressed with the script – written by Sean Conway from an idea created by Abbott – she was also worried about doing the role justice. "I was wondering why they didn't want to cast a man or a real transgender person and I guess they'd met with a lot of people and it didn't work out. And I was afraid of the pressure from the gay community or the transgender community and how they would feel, and wanting to be respectful," said Sevigny. Producer Nicola Shindler said the team had considered casting a transgender actor in the lead role. "In the end we wanted the best actor," she said.

The drama has a cinematic look that, Sky hopes, will allow it to hold its own alongside the channel's big-budget US imports, with its American star – although she takes on an Irish accent for the show – reinforcing its ambitions. However, the glamour of British television does not quite match up to those of its US equivalents, said Sevigny. "It was a lot more low-budget than I expected. Because I'd been working on Big Love for so many years with HBO, that was a very luxurious production, they had a lot of money."

"And I guess I came here and I saw the set and the crew and the Winnebagos and whatnot I was like: 'Really?'. So it was like making a small low-budget independent film for five months, which can be trying."

Hit & Miss is the latest drama to hit British screens that features a strong female lead character in a show with elements of a thriller.

"Every time you see [a female protagonist] work or see one be as special as The Killing was or as special as this is, it just automatically inspires writers to be more confident with outspoken female roles," said Abbott. "Male and female writers should just aim higher with their female characters."

Naomi Gibney, director of Sky Atlantic, said the channel was making "a conscious investment in British drama". It was about finding the "right project and the right team", she said.

Falcón, a four-part drama based on Robert Wilson's novels, will follow later in the year, while the channel also has a project about the machinations of European politics in development with Canal Plus.

Hit & Miss will run for six episodes on Sky Atlantic from Tuesday 22 May at 10pm