Question: Are both Sussex Spaniel and Lakeland Terrier native to England?

Context paragraphs:
Japanese Terrier: The Japanese Terrier (日本テリア , Nihon Teria ) is a small terrier native to Japan.  It is believed to be descended from the progeny of fox terrier types, pointers and indigenous Japanese dogs.  This dog is also known as the Nippon Terrier.  The breed is rare, even in Japan.

Sport in Sussex: Sport in Sussex forms an important part of the culture of Sussex.  With a centuries-long tradition of sport, Sussex has played a key role in the early development of both cricket and stoolball.  Cricket is recognised as having been formed in the Weald and Sussex CCC is England's oldest county cricket club.  Slindon Cricket Club dominated the sport for a while in the 18th century.  The cricket ground at Arundel Castle traditionally plays host to a Duchess of Norfolk's XI which plays the national test sides touring England.  The sport of stoolball is also associated with Sussex, which has a claim to be where the sport originated and certainly where its revival took place in the early 20th century.  Sussex is represented in the Football League by Brighton & Hove Albion and Crawley Town.  Brighton has been a League member since 1920, whereas Crawley was promoted to the League in 2011.  Sussex has had its own football association, since 1882 and its own football league, which has since expanded into Surrey, since 1920.  In horse racing, Sussex is home to Goodwood, Fontwell Park, Brighton and Plumpton.  The All England Jumping Course show jumping facility at Hickstead is situated 8 mi north of Brighton and Hove.

Russian Spaniel: The Russian Spaniel is a type of spaniel first standardised in 1951 in the Soviet Union after World War II by cross breeding English Cocker Spaniels, English Springer Spaniels and other spaniel breeds.  Physically it is similar to a Cocker Spaniel, but has a shorter, tighter coat and a longer body.  Developed and used as hunting dogs, this breed does not suffer from any major health complaints other than those normally associated with spaniels.  Popular in its native Russia, the breed was only introduced overseas in the 1990s, and is not yet recognised by any major kennel clubs.

Lakeland Terrier: The Lakeland Terrier is a dog breed, which takes its name from its place of origin, the Lake District in England.  The dog is a small to mid-size member of the Terrier family.  While independent in personality, it interacts well with owners and all family members, and is mostly hypo-allergenic (non shedding).  The breed is not widely owned in the United States.

Sussex Spaniel: The Sussex Spaniel is a breed of dog developed in Sussex in southern England.  It is a low, compact spaniel and is similar in appearance to the Clumber Spaniel.  They can be slow-paced, but can have a clownish and energetic temperament.  They suffer from health conditions common to spaniels and some large dogs, as well as a specific range of heart conditions and spinal disc herniation.

American Cocker Spaniel: The American Cocker Spaniel is a breed of sporting dog.  It is a spaniel type dog that is closely related to the English Cocker Spaniel; the two breeds diverged during the 20th century due to differing breed standards in America and the UK.  In the United States, the breed is usually called the Cocker Spaniel, while elsewhere in the world, it is called the American Cocker Spaniel in order to differentiate between it and its English cousin, which was already known as "Cocker Spaniel" before the American variety was created.  The word "cocker" is commonly held to stem from their use to hunt woodcock in England, while "spaniel" is thought to be derived from the type's origins in Spain.

Norfolk Spaniel: The Norfolk Spaniel or Shropshire Spaniel is an extinct breed of dog since the early 20th century.  It was originally thought to have originated from the work of one of the Dukes of Norfolk, but this theory was disproven after being in doubt during the later part of the 19th century.  The term was used to designate springer type spaniels that were neither Sussex nor Clumber Spaniels, and attempts were made to use it to specify a breed that would later become known as the English Springer Spaniel.

Airedale Terrier: The Airedale Terrier (often shortened to "Airedale"), also called Bingley Terrier and Waterside Terrier, is a dog breed of the terrier type that originated in the valley ("dale") of the River Aire, in the West Riding of Yorkshire, England.  It is traditionally called the "King of Terriers" because it is the largest of the terrier breeds.  The Airedale was bred from the Old English Black and Tan Terrier (now extinct), the Bull Terrier, the Otterhound and probably some other Terrier breeds, originally to serve as an all around working farm dog.  In Britain this breed has also been used as a war dog, guide dog and police dog.  In the United States, this breed has been used to hunt big game, upland birds, and water fowl, and serve in many other working capacities.

Toy Trawler Spaniel: The Toy Trawler Spaniel is an extinct breed of Spaniel which physically was similar to the King Charles Spaniel of the 16th century.  It is considered to have descended from the original King Charles Spaniel, and the older variety of Sussex Spaniel.  It was originally used as a sporting dog, but became used as a toy and show dog.  It was considered to be on the verge of extinction by 1920.  A preserved specimen is kept in Tring at the Natural History Museum.

Clussexx Three D Grinchy Glee: Ch.  Clussexx Three D Grinchy Glee (December 1, 1998-September 25, 2012), also known as Stump, was a 50 lb.  male Sussex Spaniel from Houston, Texas, who was named the 2009 Best In Show winner at the Westminster Kennel Club Dog Show.  Stump is the first of his breed to be awarded that honor and, at 10 years old, the oldest to win the prize.

Supporting paragraphs: Sussex Spaniel Lakeland Terrier
Answer: yes