Is it legal to....

That should not be any problem provided it does not restrict your vision in any way. It certainly would ours. Would certainly be illegal. 

Can't see any reason for it to be illegal unless as above.

 Looking  at  your  photos  Rosie R,  it  looks  like

A)   you  would  need  to  remove  the  table  from  the  back  of  the  passenger  seat  and  the  headrest  as  well

B ) probably  stop  the  seat  from  spinning  in  case  of  an  accident  perhaps  ??   A  foam  wedge  or  similar  perhaps.

I  have  to  ask  tho'  is  the  'moggy  mansion'  too  large  for  the  seat  to  be  right  way  round  ?? 

Moggie mansion fits on the seat just fine - just me wondering. Seemed like a good idea at the time!!