You are unlikely to find such a tour, at least as a normal commercial offering.
The likes of Rabbies provide Private Hire bespoke tours in anything from a saloon car to a minibus depending on party size- https://www.rabbies.com/en/info/private-tours/private-touring-group.
By the way it is the Lake District, not the Lake Country.
In giving Rabbies an itinerary note that their normal tours in the Lake District are quite restricted in their scope I would look at the commercial itineraries of the Mountain Goat company (which are far more comprehensive), and ask them to create one of those for you.
I doubt that will work out cheap for you, but if it's want you want...
In the Lake District, if you hire a Blue Badge guide for a day you are talking in the region of £650 a day- apparently not the full commercial rate which is around £750 a day, exclusive of your and the guide's accommodation.