Massive arrears and shortfall sale

I currently have a mortgage with Kensington which has massive arrears, my credit rating is shot to hell so I have no real prospect of getting a cheaper interest rate from them or anybody else.

Purchase price back in 2007 - £135,000
Original Mortgage amount - £121,500
Interest rate 7.85%
Expected Payment amount at £930 odd

Current property value - £82-85,000 (as per valuation by Colleys)
Current mortgage balance - £144,000
Arrears of £24,000
Current Expected payment amount £1050

I survived an eviction today by agreeing to pay them, £5,000 + £3,000 next week, + £3,000 (most of which is being borrowed from family and friends) next month in February and subsequent payments of £1,250 per month in order to clear the arrears.

Obviously the property has massive negative equity and it is just not feasible for me to try and maintain it at this cost.

What I want to do is sell the property at a shortfall and be done with it. The only hitch is, its a family property which we've had for nearly 30 years and I want to keep it in the family thus, I'd want to sell it to a family member, something I can't guarantee if I let it go to eviction and auction. I managed to get a written offer backed up with solicitor details and proof of a mortgage offer to confirm that the sale would go through at £90,000 (£5-8k above market vale) with a £20,000 cash deposit thus the amount being borrowed from the new lender would only be £70,000 thereby not affecting the new lenders interest in the property.

The problem is that Kensington are not letting me do a shortfall sale. I was told:

"sorry but with the arrears on your account we cannot consider a shortfall sale. You must either make an arrangement to clear the arrears off or we will go down the repossession route"

No option of me discussing possible payment plans to clear the shortfall difference whatsoever. just simply the above ultimatum ,that's it.

What I want to know, is how can I convince Kensington to allow me to do this shortfall sale??