One man was killed and three are still missing after a former boiler house partially collapsed during preparatory demolition works on 23 February.
Thousands of tonnes of material still remains at the site.
Managing Director Mark Coleman tweeted he was "so disappointed" at the decision "which prevents us from recovering our men".
In a statement, Coleman & Company said: "We have now reached a stage where we will be handing over the remaining recovery operation to another contractor within the next few weeks. This is of course hugely disappointing as we all wanted to recover our friends and colleagues and return them to their families.
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"We wish to make it clear that this decision in no way diminishes the excellent work that everyone involved in supporting the recovery has done. The praise we have received from RWE, the Police and HSE for how we have conducted the recovery since it began, in these tragic and difficult circumstances, reflects the dedication and commitment we have to each other and the business.
"It has been explained to us that this decision has been made for reasons of safe-guarding employee welfare and the preservation of critical evidence. We understand these reasons and our immediate focus is to ensure that we continue with the recovery operation for as long as we are permitted and at the same time, work collaboratively to facilitate a seamless transition so that the recovery operation going forward proceeds without delay."
The company will remain on-site as Principal Contractor over the coming weeks before handing over operations to a new contractor.
(LM)
