As all the contents are second-hand they will have a surprisingly small market value, so the other three children need to take that into account - their 'fair share' is unlikely to be much, unless the furniture is sought-after antiques. And even then it might not be as much as they expect.
I regularly attend my local auction house, and quite a bit of what they handle is house-clearances. What do I mean by small market value? Sofas for £10 - £50, Dining table and 4 chairs for £20 (if they sell at all) fridge-freezers/ cookers / washing machines / tumble dryers for £20 - £30. Dining tables, sideboards, display cabinets frequently don't sell; or are bought by landlords for £4 to furnish their student rentals. It breaks my heart when I see a beautiful mahogany table go unsold and you suspect it will become firewood.
Specific examples - I bought a beautiful wool rug for £12 that must have cost the owner £250+ to buy new. A bookcase for £15 that I would estimate at £150. Coffee tables for £5. I did pay £80 recently for a good solid bookcase/display cabinet with glass doors - something similar from a local furniture shop is £800.
Second-hand furniture sells for far, far less than it cost to purchase new, even if the item is only a couple of years old and in good condition.
So, for the adult child who wishes to stay in the house with all the furnishings, I think it would be fair for their siblings to be realistic about the value of the furnishings. It would be fair for the adult wishing to retain the furnishings to pay their siblings in lieu of their share of the furnishings. You all need to make a list of the contents and their realistic market value (remember - not much at all). Discuss the items of sentimental value, and apportion fairly.
It would also be a good idea for the siblings to consider how much it costs to have goods transported. Generally I can get stuff in the back of my car, but a couple of years ago we had to get a man&van, his £60 fee was more than the cost of my purchase. So whilst there may be a temptation to say 'well I really need a new fridge so I'll take that', it could cost them dear to transport.