As I said the day rate they are charging clients is £350-400.
Unfortunately I see less than 50% of that.
Way back in the day I worked for a year resourcing staff for IT projects. 15 years ago £350 would have got the client a standard BA or a Project Co-ordinator.
The PM charge rate to clients started at £450 and went as high as £1250.
It was not uncommon to use a high rate PM to fill a Low rate PM role if we where stuck for resources. Which might be happening in your scenario. Or you are not doing a PM role, but more a PC or Project officer role.
My IT contracting days are long over, I have hung up my spurs and have gone permanent.
My last day rate offer was £400 at a bank in 2010. I turned it down to get a less well paid, but perminant job.
It's all horses for courses.