It's so much easier to just sell, rent and then buy.
It seems far too difficult to coordinate the buying and selling. Too much stress all at once.
Rent a garage for the furniture (or a place with a garage).
You then have the great advantage of being a cash buyer for a new place. You can jump on an opportunity, get a bargain - and avoid being let down.
Last time we moved, the house we really wanted was quickly sold. We put a note through the door, with our contact details, just in case the sale fell through.
For some reason, the 'buyer' went abroad and couldn't be contacted. The seller lost patience and sold to us - at a discount - as he'd moved and had an expensive bridging loan.
He had no estate agent fees to pay, though - as we hadn't used them - so everyone was happy.