Science Fantasy Stories by Angus Allan, J.H. Tead, Ross Trapnell, Malcolm Shaw, M.S. Goodall, J. Williams, Lloyd Williams, Richard Grimston.
The story mentioned in the question is called "The Dream-Makers" by Malcolm Shaw.
Other stories in the collection include:
Master of all the world! by Angus Allan - a bullied and disenfranchised child is given the ability to destroy all of humanity through mental abilities by aliens looking for a planet to colonise.
The last day on earth by Richard Grimston - a pre-human humanoid civilisation on earth has just 24 hours left to live, but there's still time for a school trip to a science lab...
In the new beginning by Angus Allan - a space cruiser picks up some humans in hibernation who have been asleep for a very long time.
Old MacDonald had a space farm by M. S. Goodall - a isolated farmer of Wrigglets goes mad with loneliness.
The specimen jar by M. S. Goodall - a colonisation transport ships passenger has a very bad dream that turns true when they wake up.
In the eye of the beholder by Angus Allan - a group of explorers make a fatal mistake when meeting the locals.
Break out on Pris-Sat 9 by Ross Trapnell - a group of prisoners break out from their prison, but they have a traitor amongst their midst.
Sneak attack by J. H. Tead - an old space cruiser manages to beat overwhelming odds when they suddenly face the entire enemy fleet.
Alien holiday by Lloyd Williams - a holiday planet is built between Earth and Mars, but as one boy's holiday progresses, fewer and fewer of his fellow holiday makers seem to be human.
The turn of a card by Angus Allan - several explorers on an alien planet are trapped in a cave by a huge predator, and they draw cards to see who has to act as a diversion for the rest to escape.
Feeding time by M. S. Goodall - a professor tames a seemingly untameable alien humanoid species by giving them sweets, but it all goes horribly wrong when two visitors from Earth get curious.
Doomlist by Angus Allan - a military and scientific base on an alien planet is about to be overrun by an unstoppable local predator, but there is only one ship left which cannot carry everyone and one man thinks he should be on that ship above everyone else.
The Dream-Makers by Malcolm Shaw - a boy starts passing out and having dreams of a post-apocalyptic world, but gradually realises he has more control over the world than most.
Sinkhole One by M. S. Goodall - a crustacean farmer is given government quotas he cannot meet, and when he is killed for resisting his vengeance is unleashed.
Something in the basement by J. Williams - a local man becomes the centre of concern when he displays odd behaviour, and when someone decides to break into his house to investigate, all is not as it seems.
The 'S' stone of Sangros by M. S. Goodall - a group of mercenaries are paid to blow up an officially recognised galactic monument, a massive stone carved into the shape of an S, but rather than destroying it they accidentally awaken something terrifying.
A Question of time by Angus Allan - a group of explorers find themselves deep in earths past after accidentally travelling through a time warp - or do they?
Hi-Fly by M. S. Goodall - a new sport is invented using mutated giant flies, but one bully isnt happy when he loses his match and blames his fly for his loss.
The jokes on you by Malcolm Shaw - a man is picked to appear on a sadistic TV show where your dreams can come true, but only if you overcome your worst fears.
Arkadya by Ross Trapnell - a group of space explorers find a colony of people seemingly dating from the 17th century, but it soon becomes clear that they are never supposed to leave.
Nightmare by J. H. Teal - a group of space explorers discover an alien artefact but are warned off with ever increasing intensity by the artefacts defences. When they finally reach the centre, they discover it was a prison all along and only a crew members cold saves the day.
H.E 11 and back by Malcolm Shaw - a group of prisoners being shipped to a prison planet escape cryosleep and take over the ship.