Jensen was born in Nykøbing Falster, and played for a number of Danish lower-league teams, making his debut for the Danish under-19 national team in November 1995. In May 1996, he was loaned out from Danish second division club Nykøbing Falster Alliancen to Næstved BK in the Danish Superliga. He played four games while at Næstved, but could not prevent the club from being relegated at the end of the season. He moved permanently to Superliga club Lyngby FC in June 1996, signing a contract alongside later Danish international Dennis Rommedahl.
He played two years at Lyngby before moving to play in England in July 1998. He was bought by First Division (now Championship) club Bolton Wanderers in a deal worth 1.8 million DKK. While at Bolton, he debuted for the Danish national team in March 2000.
In July 2000, he moved to Premiership club Charlton Athletic for £4 million. He was called up to the Danish squad for the 2002 World Cup, where he made a single appearance as a substitute. In February 2003, he scored a hat-trick in a 4–1 friendly win against Egypt; one of the goals was scored from a direct free kick. He also represented Denmark at the 2004 European Championship, where he took part in three of Denmark's four matches.
After more than 100 games for Charlton, in July 2004 he moved to the Addicks' London rivals Fulham in a transfer deal worth £1.25 million. He made his Fulham debut at Manchester City on 14 August 2004. He spent three years with Fulham, but was plagued by injury and on 17 May 2007, Fulham manager Lawrie Sanchez decided to release him; Jensen claims his release was inevitable because he did not fit into Sanchez's long ball tactics. After three years with repeating injuries, he chose to end his professional career on 25 August 2007.
Fish started his career in his native South Africa under the guidance of renowned coach Steve Coetsee, playing for Arcadia Shepherds, an amateur team based at the Caledonian Stadium in Pretoria. He was spotted by then Jomo Cosmos coach Roy Matthews and turned professional as a striker. It was at Cosmos that he was converted into a central defender and went on to become one of the most promising defenders in South Africa at the time.
In 1994 Fish was signed by Orlando Pirates after Cosmos were relegated. At Pirates he arguably played the best football of his career under the tutelage of Mike Makaab. He also won the league championship at Pirates, as well as the BP Top Eight Cup in 1994, the 1995 African Champions League and the 1995 Bobsave Super Bowl (then the premier cup in South Africa). In 1996 he was part of the history making South African national team to have won the African Cup of Nations at the first attempt after South Africa's readmission to FIFA in 1992.
Soon foreign scouts came knocking and he was signed by Lazio of Italy, after he turned down an opportunity to play for his boyhood club, Manchester United. However he did move to England after just one season at Lazio to become the highest paid player at Bolton Wanderers. Fish was a mainstay in Bolton's back four for much of their first season back in the Premiership, he received praise from both team mates and those whom he played against, most notably Manchester United forward Andrew Cole. Despite Fish's efforts Bolton were relegated on the last day of the season despite having accumulated 40 points, normally enough to stave off the drop. Once playing back in the lower leagues Fish applied himself well, quickly gaining a cult status amongst the Bolton faithful, backed up by his nickname "Feesh", and a particularly eyecatching headgear in the shape of a giant Blue fish being made available in club stores. However, new suitors soon came calling, and only after the appointment of Sam Allardyce did Fish's star begin to fall in the North of Lancashire. Fish soon followed his Danish team mate Claus Jensen and at Alan Curbishley's second time of asking moved to Charlton Athletic in a £700,000 move in November 2000. "The Big Fish" as he was affectionately known throughout his playing career went on to make 102 Premiership appearances for the Addicks, scoring three times.
In 2005 he began to fall out of favour at Charlton. He went on to have a very short loan spell (45 mins) at Ipswich Town in the 2005–06 season but a severe cruciate ligament injury led to Fish announcing his retirement.
Fish returned to football when he signed a six-month contract with his first club Jomo Cosmos in early 2007 but did not play an official game due to his low level of fitness.
Born in Lewisham, England, Barness started out as a trainee for Charlton Athletic. It is to be noted that in his first spell at Charlton he scored Charlton's opening riposte after going 3–0 down at Newcastle, this strike was the goal of the match. Charlton went on to win the match 3–4 and this has been voted in the top 20 Charlton matches of all time.
His potential was spotted by a youth-scouting Chelsea side in 1992 and signed for £350,000— though some have said Chelsea only signed Barness after failing to sign his team mate, Scott Minto. During the four years which he spent at the club however, his chances of league starts were taken away from him at every possible opportunity. Thus, after just nineteen appearances in four years, he was loaned out to Middlesbrough (in August 1993) and Southend United (in February 1996).
Barness left Chelsea in August 1996, and returned to Charlton Athletic for a fee of £165,000. He was an important and regular part of the Charlton team, managed by Alan Curbishley. In his first season back at The Valley, he was a virtual ever present and a top performer in a Charlton side struggling after the sale of Lee Bowyer. Barness suddenly left the first team in 1997 being replaced by Mark Bowen at left back and occasionally Paul Konchesky, and only made a handful of appearances from then on many at right back. Although Mark Bowen was an excellent performer for Charlton in the 97/98 season, many Charlton fans were perplexed by Anthony's replacement as he'd been a very reliable player. Alan Curbishley was quoted at the time of dropping him, that he'd been virtually ever present the previous season and appeared close to burn out. Though the fans saw a minimal drop off in form, it retains a mystery why he fell out of favour with Alan Curbishley.
On the move again in 2000, he went to Bolton Wanderers on a free transfer deal and was initially a regular starter in Lancashire, but was soon relegated to starting only in Cup competitions – which manager Sam Allardyce often left to the second team. In his second year Barness made the right-back position his own, and became a fans favourite due to his effort for the cause. Barness continued to play for the first team over the next couple of years. He was set to move on loan to West Ham United in February 2004 but was recalled within 24 hours after Bolton suffered an injury crisis. He then played a vital role for Bolton as they set a record for the most consecutive wins by their club.
After being released by Bolton in May 2005, he joined Championship side Plymouth Argyle on a free transfer the following month. He impressed fans with solid performances throughout his first season with Argyle. He was released from his contract at Plymouth by manager Ian Holloway on 30 January 2007.
Others who were both an Addick and a trotter include - Neil Redfearn, John Salako, Mike Salmon, Andy Todd and Charlie Wright.