Overhanging Stud Frame?

[Brizlix]

In my Kitchen I have a small alcove roughly 400mm deep. Our boiler and gas meter is fitted in this alcove. Both are then surrounded by some hacked up cupboard units which have no bottoms and cupboard doors fitted. Then under the boiler to the floor there is a plywood 'wall'. This takes up about 300mm depth of the alcove and has a radiator fitted to it. The cupboards extend out over the fake wall but also out past the edge of the alcove

It all needs to come out as access to the boiler is shocking and the plaster is cracking where the sheets of ply meet. Plus we're fitting new kitchen cupboard doors.

I want to keep the false wall (replacing it with plasterboard) as it covers a load of ugly pipework. But was thinking it would be best to replace it with a solid stud frame. As it should be more solid than whats already there.

But I'm concerned that with a P shaped frame the top will want to rotate forward and will start to droop. Especially as one of the front corners will have nothing to take it's weight. I can only fix it to the wall on the left hand side, the back and a bit of the right hand side.

Any advice to ensure it can support itself?

 

[Brizlix]

To try and help this is a rough drawing of what the frame would look like from the side. No noggins or supports in this picture.

I could actually secure the top horizontal to the joists in the ceiling above.

 

[Tigercubrider]

a photo would help.
your diagram has no reference points. it could be a floor plan for all we know.