Born in Birmingham, Wrench grew up in South Africa, where he began his career in journalism after a degree at Rhodes University. After newspaper work on the Johannesburg Sunday Express, he spent much of the 1980s reporting on the anti-apartheid protests of the era. His first radio job was with Johannesburg-based Capital Radio 604, which provided the first independent source of broadcast news in South Africa.
At Turnstyle News, an independent radio news agency, Wrench reported for the Canadian Broadcasting Corporation, National Public Radio, the Australian Broadcasting Corporation and the UK-based Independent Radio News and London Broadcasting Company.
In recently published diary extracts, Wrench has revealed the personal thoughts behind his South African reporting. In the aftermath of one police shooting in Soweto in August 1986 he wrote: "A kid showed me welts from shotgun wounds. I came away mentally wounded myself. Cry for the country! I throw an ANC thumbs-up salute through the sunroof [of the car]. It is less a gesture than a commitment, quite frankly. This after once pleading non-involvement. Enough, no longer."
Reporting on demonstrations in Windhoek, Namibia, in September 1988, he was among those beaten up by police.
In 1989, he moved to London and joined the BBC as a reporter for the Today programme. In 1990, he was among the reporters at the prison gates when Nelson Mandela walked free. Wrench reported from a wide variety of other locations for BBC Radio including Jerusalem, St Petersburg, Bucharest, Kiev and Bosnia.
Wrench was the co-host of Out This Week, a weekly gay and lesbian news programme on BBC Radio 5 Live for which he won a Sony Radio Award. He won a New York Radio Award for his 1998 Radio 4 documentary Aids and Me, while also regularly co-presenting the Radio 4 programme PM. Wrench later worked as a culture reporter for PM, interviewing leading artists, performers, playwrights and novelists as well as reporting regularly from the Edinburgh Festival.
Nigel Wrench is one of the few journalists to have met and interviewed Banksy. The graffiti artist spoke to Wrench for PM at the opening of "Turf War", the first Banksy exhibition in London in 2003.
Wrench publicly announced his status as HIV-positive in 1994, in a speech while accepting his Sony Radio Award. He wrote extensively about living with HIV and AIDS, including a regular column for the Pink Paper  and made a television documentary called From Russia With Love for BBC3 in 2003.
He has since left the BBC again, and in February 2015 released ZA86, a limited-edition cassette, through specialist label The Tapeworm. A sleeve note says: "apartheid South Africa, 1986, through the headphones of a young radio reporter".
- Cowell, Alan. "WINNIE MANDELA JAILED FOR RETURN TO SOWETO HOME". New York Times.
- Wrench, Nigel. "ZA86". Retrieved 2 February 2015.
- Vries, Da'oud. "Nothing Changes" (PDF). The Namibian.
- Manoim, Irwin (1996). You have been warned : the first ten years of the Mail & Guardian. London, England: Viking. p. 35. ISBN 0670867926.
- Popham, Mike (1990). The Best of From Our Own Correspondent 1989/90. London: Broadside Books. p. 127. ISBN 0951562924.
- "Aids and Me". BBC News.
- Elmes, Simon (2007). And Now on Radio 4. London: Arrow Books. p. 217. ISBN 9780099505372.
- Mulholland, Tara. "Fringe festival sounds a somber note". New York Times.
- "Banksy's Bristol". BBC Bristol. BBC. Retrieved 11 March 2015.
- "Pills, Patients and Profits". BBC World Service. BBC.
- Buchanan, Justine (1996). "London Bridges". POZ. Retrieved 2009-02-08.
- Watney, Simon. "Imagine Hope".
- Wrench, Nigel. "Living with HIV in Russia". BBC Nes. BBC.
- "Sex on the Edge". The Guardian. Guardian Media Group.
- "Presenter cleared of raping man". BBC News. BBC.
- Bath, Tristan. "Spool's Out: Tape reviews for March". The Quietus. The Quietus. Retrieved 11 March 2015.
- "The Tapeworm presents .... ZA86". The Tapeworm. Retrieved 2 February 2015.