There are two must-see photographic exhibitions on in London now – unconnected apart from their use of black and white.

The Don McCullin retrospective at Tate Britain is on until May 6. It starts with his early works in London, including the fantastic The Guv’nors, an image of local sharp-dressed lads posing in the framework of a building. It was that photo which got him seen by the Observer and he has been in demand since.

The exhibition guide features a timeline of world events and conflicts which had an impact on McCullin’s life and career. He apparently is haunted by the fact he is known as a war photographer, but there are many images of conflict and suffering here. Each section on a new conflict he has photographed has a useful introduction explaining it and putting it in context.

There are many shocking images of injury and death, and captions explaining what McCullin was doing at the time of some of the photos, including a photo of a man who was injured in an explosion which he was also struck by, but the man later died. There are haunting close up faces of shock and fear around the world from Biafra, Cyprus, Congo, Ethiopia, Cambodia, Beirut, Iraq and more. Quotes from McCullin reveal how hard he found it to be a witness to their horrors, but saw his role to capture and record it.

McCullin also happened to be in Berlin when the wall was going up, and photographs its building, and civilians and soldiers on both sides. People wave across to family and friends they will be separated from for decades.

On visits home, McCullin captured Bradford and the North as the section is called. There are images of people living in poverty, and also homeless people in the East End of London, showing suffering isn’t always a long way from home.

The exhibition ends with landscapes, still in black and white, but bringing peace to the photographer and hopefully the visitor.

At the Hayward Gallery and also on until May 6, is an exhibition of photos by Diane Arbus, taken in New York City where she was born in 1923, and killed herself in 1971.

These photographs are smaller and the gallery emphasises there is no set route around the exhibition, or chronology to it. The images are displayed on pillars that visitors drift around and have to get close to, and there are photo titles but no more information. Arbus was clearly attracted as a subject to many of those on the fringes of normal society, as well as the woman wrapped up in a fur coat on the bus.

The people photographed are all in New York, or Coney Island, where the idea of a fun resort is tested to the limit. There are many photos of female impersonators before or after their shows. There is a little boy with a toy hand grenade in Central Park, and spooky looking identical twins. Eddie Camel, Jewish Giant, taken at Home with his Parents in the Bronx in 1970, stoops to fit in the room with his normal-sized mum and dad. Another man is covered with tattoos, and a dwarf woman cleans her house.

It’s a completely different exhibition to the McCullin one, but one which also shows us a lot about the variations of humanity.