Nikos, we had a similar situation, we were assessed for dd1, given a respite carer via SS, who was then removed from their employ due to alleged child protection issues.... We then had no-one for months.
I emailed our MP, who took up the case - it was pretty black and white really, SS had assessed us as needing certain hours, but were failing to provide the care. MP wrote to Head of Children, School and Families at local council. We also ended up on the website of a national paper, with the story.
It took months, it was stressful, in fact it was horrendous, I got fobbed off time and time again, but I refused to give up, I called/emailed EVERY DAY (!) and I have to say that the MP and his PA were superb.
We now have the respite - dd1 went to the lady's house for the first time last Friday for an overnight stay.
Good luck.