I'm a solicitor and I'm dealing with this on a daily basis.
And, yes, unless you have a parent, friend, child who is happy to let you move in with them or let you move in to a house vacated by parent in nursing home or some similar situation, you won't be able to complete the sale of one house and the purchase of another in one seamless transaction. There do seem to be short term rental opportunities available.
It is safer to complete each transaction separately. Too many people got quite badly burned when they contracted to buy another house on the strength of signed contracts for their own. When that contract collapsed, they were stuck with the purchase.
mf