In the final episode:

The Holmes brothers are sent to investigate some very strange happenings at a military base.  Among the suspects is Captain John Watson, an army doctor.  When things take turn for the stranger, the younger Holmes is forced to take Captain Watson into his confidence, and the doctor proves himself to be a surprisingly capable ally.

The solution to the mystery has repercussions in the highest echelons of the Brititsh government.  Mother decides that she’s had enough and resigns.  The elder Holmes brother resigns from field work and takes on her title.  (Yes, he’ll be Mother.)

Meanwhile, Mother, or Mrs Hudson, as she is now known, retires to a ground-floor flat in central London and leases the flat upstairs to Captain Watson and Holmes the younger, who have also decided to embark on a new line of work.

After being invalided home from Afghanistan, John takes up baking to keep busy when his therapist suggests that he find a hobby and blog about it.  He’s completely gobsmacked when he is accepted onto the show.  

Sherlock takes up baking to keep his mind off the drugs (so many white powders!) Lestrade submits his name for the show and Sherlock is completely nonplussed when he is accepted, but why not, he’s bored.  

Sparks fly immediately when the boys meet.

Mrs. Hudson wins the final Bake-off, but everyone’s okay with that because everybody likes her.  During the final celebration, she lets the boys know that there’s an empty flat in her building (upstairs from Speedy’s Bakery) They never do need that second bedroom, and they bake and solve crimes and live happily ever after.