Most likely the Building regulations will be ok with your proposals with some caveats added it - that of extra fire safety systems. Have you already submitted the plans ?
The definite answer is a No. For the former query, one can build a fire resisting storage under the fire stairs with the same resistance as that the stairs. This will be allowed when you have more than 1 fire escape stairs.
For the latter query, No, you can not build a cabinet under your only fire escape stair/route.