I am not aware that the term "tolerably safe" is defined anywhere in MoD policy or regulation. However, it has come to be used, in the field of defence aviation at least, in roughly the following manner. To say an aircraft is "tolerably safe" is the same as saying that the risk associated with operating that aircraft is "tolerable" ("tolerable", as applied to risk, is a term that is well-defined in MoD policy and regulation). This is a right pain because not only does this lead to the confusion between "tolerably safe" and "safe" (which are not equivalent, as pointed out above) but also, the term "tolerably safe" is used in other contexts and industries to mean "the risk is tolerable and ALARP" (which is much closer to the MoD definition of "safe").
The distinction between "tolerably safe" (meaning the risk is "tolerable") and "safe" is not, in my opinion, well understood within the MoD. I find it very plausible that Des Browne may have been misinformed by the MoD in respect of any statements he made concerning whether or not the Nimrod in question was "safe". I would expect QinetiQ to very well understand the distinction, though I would think it regrettable if they used the terms "tolerably safe" or "acceptable" without explicitly defining them (the latter was probably used in a generic sense rather than in the sense of "Broadly Acceptable", which is also a well-defined term).
Also, some reference has been made to Def Stan 00-56, "Safety Management Requirements for Defence Systems" (from which the MoD definitions of "safe", "tolerable" and "broadly acceptable" have been taken in preceding discussion). This standard is not strictly applicable to safety management by the MoD itself. Instead, the standard is intended to specify requirements for safety management by contractors to the MoD. For example, BAE or any other supplier of safety-related military equipment.
The document that specifies MoD safety management requirements, at least for the IPTs (Integrated Project Teams) that procure and administer MoD equipment, is the Project Oriented Safety Management System (POSMS). It can be found at:
http://www.asems.mod.uk/posms_manual.htm
It shares many of the principles and definitions of Def Stan 00-56, inheriting many of the definitions directly. It is a much larger document but also provides a lot of very readable (for the layperson, I would have thought) guidance.
In my opinion, the distinction in the scope of applicability between Def Stan 00-56 and POSMS is also not well understood within the MoD and its contractors.