Their parents came from the Penrith area and father was a lawyer. He managed in his early twenties to obtain a good appointment with the Lowther estates and acted as agent for a large section of Lord Lowther's properties, especially in West Cumberland (what we now know of as West Cumbria). With the job came a splendid house in Cockermouth, hence it was there that William and Dorothy, along with siblings, started life.
The property is now known as Wordsworth House and is in the keeping of the National Trust, and open to the public.
See more about the Wordsworth birthplace on the main Around-England site.