Why were there dementors in Little Winging in of Harry Potter and the Order of the Phoenix?

Dolores Umbridge sent them. The rest of the ministry had no role in the dementors going to Little Whinging. However, if they did, it was never revealed. However, Umbridge used other forms of torture against the ministry's wishes, which includes the blood quill and almost using Crucio on Harry. She sent them most likely because she knew that Harry would use magic to defend himself (she probably heard about his use of the patronus spell at the quidditch match against Ravenclaw). It would be used to discredit Harry and Dumbledore since she didn't expect any other magical person to come to his aid (besides Dumbledore, who was looked upon as as loony as Harry). She expected no one to believe that there were actually dementors in the muggle world and that it would just justify that fact that Harry was a crazy, attention seeking liar. However, if she had heard wrong and Harry didn't know the spell or had his wand with him, he would have been worse than killed by the dementors.

Dolores Umbridge.

The Ministry were trying to quash any rumours that Voldemort had returned, so she sent the Dementors after Harry in the hope they'd "silence" him.