One person, one will
A will can only ever dispose of the estate of the person who signs it. There is no practical "joint will" covering two people — so yes, both spouses (and both civil partners) each need their own. Each will deals with that person's own assets and their own wishes: who acts as executor, who would care for the children, and where everything goes.
Why "my spouse gets it all anyway" is wrong
Many couples assume everything automatically passes to the survivor. Jointly owned assets often do — but anything in your sole name follows the intestacy rules if you die without a will, and those rules hold a surprise. With no children, a surviving spouse or civil partner does inherit everything. With children, the spouse receives the personal belongings, the first £322,000, and only half of what remains — the children share the other half, which can force a house sale or leave a spouse cash-poor at the worst possible moment.
Mirror wills: the usual answer for couples
Most couples solve this with mirror wills— two near-identical wills, typically leaving everything to each other first, then to the children. Each person signs their own document, and each keeps the freedom to change their own will later; the "mirror" is a choice, not a lock.
Sorting both takes less time than you think
Two wills, one evening. You can each make your will in about 15 minutes with SwiftWill — a one-time £35 per will, with free updates for life and no subscriptions or upsells.