25mm MDF Strong Enough?

[Harrier23]

Hi,

I'm looking to build some storage in my small utility room which goes up the side of my washer/dryer and then over the top.

I will need to find a way of securing the horizontal storage to the empty wall which is a cavity wall and the depth of the unit I will make will not be deep enough to fix to the studs.

My question is, if a place a 25mm sheet of MDF against the empty wall and fix the unit to that, will it be strong enough?
There won't be huge amounts of weight being stored in the horizontal storage, but maybe 10-15kg.

I've attached a rough diagram of that helps

 

[freddiemercurystwin]

Got a photo of the area in question?

 

[Harrier23]

Here you go.

I'll be replacing the unit on the right and will also be building along the top which will connect to the side unit.

Its the wall on the left that the 25mm MDF (or alternative) will be placed up against to support the horizontal unit

 

[foxhole]

Just build unit against wall a few fixings will secure to wall whatever its make up. 25mm MDF is way OTT.
(18mm MDF is fine)