I read the book in the US in the 1970s, I thought it was called "Out There" but can't find it anywhere. It was about a space rocket struggling in some way, had a small crew I think of young people, one was named Ash or Ashley... And either he or one or all of the crew suffered from radiation sickness. I can't remember much more detail but it had a big impact on me as a young teen.
This sounds like "Space Hostages" by Nicholas Fisk. It was first published in 1967, which fits with your recollection of reading it in the 70s. A lieutenant takes control of a space ship and uses it to kidnap a group of children. One of them, a bit of a mummy's boy, was called Ashley. In the take off, the lieutenant overloaded the nuclear-powered motors, and as a consequence received a high radiation dose. He eventually dies of radiation sickness, leaving the children to bring the craft home themselves (with radio guidance from Earth).