I don't think you realistically can enter consulting at 85K. Not devaluing what you do but at this level you'd be expected to do some business development and as Rollercoaster says difficult without any previous Consulting experience or commercial experience for that matter. 85K depending on company is typically Senior Manager (but this could be called Director in some Niche companies or even Principal)
However, given you are a Deputy Finance Director a potentially more lucrative move might be the interim / contracting market - have you considered this ?
If you are Deputy try and get an FD role even if you move to a smaller Trust then the Public Sector interim roles would open up.
Of course if money is not the driver and you are prepared to go down a grade / money then you may get some success.