Question: What is the name of the English football club that had played in Runcorn, Widnes, and Prescot during its existence and who footballer Danny Byrne had previously played for?

Context paragraphs:
Runcorn Town F.C.: Runcorn Town Football Club is an English association football club based in Runcorn, Cheshire, England.  After spending most of their years in the West Cheshire League, they were elected to the North West Counties League in 2010 and are currently in the Premier Division.  Their home ground is Pavilions in Runcorn.  Runcorn Town also has a Junior Section with six junior teams under the club's umbrella.

Danny Naughton: Daniel "Danny" Naughton (birth registered January→March 1925 – death unknown) born in Prescot district.  was an English professional rugby league footballer who played in the 1940s, and 1950s, playing at representative level for England, and at club level for Widnes, and Warrington, as a prop , i.e. number 8 or 10, during the era of contested scrums.

Liverpool Stanley: Liverpool Stanley was a semi-professional rugby league club from Liverpool, England.  It was renamed Liverpool City in 1951, but was otherwise unrelated to the original Liverpool club of the same name.  The club's origins date back to 1880 when it was founded as Wigan Highfield.  Although the club was best known for its years in Liverpool, the club relocated numerous times, and were known as London Highfield, Huyton, Runcorn Highfield, Highfield, and eventually Prescot Panthers throughout their existence before being eventually wound up in 1996.

Ray Owen: Raymond "Ray" Owen (birth registered July→September 1940 — 5 February 2006 (aged 65)) birth registered in Prescot district, was an English professional rugby league footballer who played in the 1960s, and chairman of the 1980s, playing at club level for Widnes, and Wakefield Trinity (Heritage № 694), as a scrum-half/halfback , i.e. number 7, and was chairman for Widnes from 1987 to 1991.

Danny Byrne: Daniel "Danny" Byrne (born 30 November 1984) is an English footballer who most recently played for Ashton United.  He was born in Frimley, Surrey, and plays as a forward.  He has previously played for Manchester United, Hartlepool United, Reading, Southport, Chester City, Droylsden, Runcorn FC Halton, Leigh RMI, Witton Albion, Newcastle Town, Mossley and Flixton.  He signed for Ashton United in September 2009.

Runcorn Linnets F.C.: Runcorn Linnets F.C. are an English football club based in Runcorn, Cheshire.  The club currently plays in the North West Counties League Premier Division , the ninth tier of English football, and is a full member of the Cheshire County Football Association.  The club is run by a trust, which is an Industrial and Provident Society, and is registered with the Financial Services Authority.

Colin Hutton: Colin C. Hutton (May 1926 – 3 February 2017) born in Prescot, Lancashire (now Merseyside), was an English rugby union and professional rugby league footballer who played in the 1940s, and 1950s, and coached in the 1950s, 1960s, and 1970s, playing at club level for Widnes, and Hull, as a fullback , or centre and coaching at representative level for Great Britain, and at club level for Hull Kingston Rovers, he was the Rugby Football League President for 1992–1993, and was the President of Hull Kingston Rovers up to his death.

Harry Owen (rugby league, Widnes): Harry 'Ginger' Owen (birth registered during January→March 1907 — death registered during January→March 1966) birth registered in Prescot district, was an English was a chemical worker and professional rugby league footballer who played in the 1920s, 1930s, and 1940s, playing at club level for Widnes, as a wing , i.e. number 2 or 5, his death was registered in Prescot district.

Runcorn F.C. Halton: Runcorn F.C. Halton was an English football club that played in Runcorn, Widnes and Prescot at various points during its existence.

Prescot BI F.C.: Prescot BI Football Club was an English association football club based in Prescot, Merseyside.  They competed in the FA Cup and FA Vase.

Supporting paragraphs: Danny Byrne Runcorn F.C. Halton
Answer: Runcorn F.C. Halton