Fitzpatrick attended St Thomas of Canterbury, Sheffield St Mary's Roman Catholic High School, Chesterfield and Woodhouse Grove School, in Apperley Bridge, City of Bradford. She has three older brothers named Chris, Peter and Michael, who are all keen tennis players themselves and who are very supportive of their sister. Growing up, she played her tennis at Beauchief Tennis Club and at Graves Tennis Centre. She enjoys learning languages, scuba-diving, reading and music, especially Rihanna and Beyoncé. She also enjoys reading and watching Harry Potter. Within the tennis world, she admires Roger Federer, Pat Rafter and Mansour Bahrami.
Anna likes to play aggressively, coming to the net as often as possible. When at the back of the court she is always looking for opportunities to attack and often tries to serve and volley to change the pace of the match. According to Anna, her volley is "what [her] whole game is built on" and her least favourite surface is clay.
Anna's first match on the junior ITF circuit came in July 2003 and her last in June 2007. During her four-year junior tennis career, she did not reach any tournament finals but reached the semi-finals of three tournaments, one of which was the 2007 Wimbledon girls' tournament where she lost to eventual champion, Urszula Radwańska, 6–7(3) 3–6. She also lost in the quarterfinals of a total of five tournaments. Her win-loss record for singles competition was 25–26.
As a junior doubles competitor, Fitzpatrick won one tournament (partnering Jade Curtis) and was a runner-up in another. She was also a semi-finalist four times and lost in the quarterfinals in nine tournaments. One of the tournaments in which Anna became a quarterfinalist was in the 2007 Wimbledon girls' doubles tournament with Jade Curtis. She ended her junior career with a doubles win-loss record of 27–28. Her career-high combined singles and doubles ranking was world No.180 (achieved 9 July 2007).
Anna Fitzpatrick played her first professional match on the adult ITF circuit in September 2004 when she attempted to qualify for the $10,000 event in Manchester. She lost in the second round of qualifying. Her only other tournament during 2004 was the $10,000 ITF in Bolton where she also lost in round two of qualifying. She finished 2004 without a world ranking.
2005 saw Anna play in a total of eleven ITF tournaments. She lost in round two in two tournaments, the first round in three and the qualifying stages a total of six times. Her very first year-end ranking was world No.1102.
In 2006, Fitzpatrick made very little progress on the ITF circuit until August when she won her first ever ITF title in the $10,000 event in Ilkley without losing a set in the entire tournament. She beat fellow British teen, Anna Smith, in the final, 6–4 6–3. She carried this momentum over into her next tournament (Wrexham $10,000) where she reached the semi-finals and she also made a run into the final of her next tournament, the $10,000 ITF in London. She was beaten by Nadja Roma, 3–6 3–6, in the final. She finished the season with her ranking at world No.676.
In March 2007, Anna reached the third ITF singles final of her career in Sunderland $10,000 where she lost to Gaelle Widmer in straight sets, 4–6 1–6. In April she became a quarterfinalist in the $10,000 event in Bath and one month later she lost in the quarterfinals of a $25,000 event in Antalya as a qualifier. June saw Fitzpatrick make her debut on the WTA tour when she was given a wild card into the qualifying draw of the DFS Classic. She faced American, Lilia Osterloh, in the first round and was unable to capitalise on her one set lead, eventually losing, 7–5 3–6 1–6.
Nevertheless, she earned a wild card into the qualifying event for Wimbledon one week later by winning two matches in the LTA wild card play-offs. She managed to beat Junri Namigata, a player ranked 278 places above her, in the first round of the qualifying tournament with a score of 7–5 6–0. The No.8 seed in the qualifying tournament, Mathilde Johansson, proved too much for Fitzpatrick in round two and Anna lost, 1–6 2–6. In July, Anna reached the semi-finals of a $10,000 event in Calgary (where she won the doubles tournament to give her the first doubles title of her career) and in September she reached the semi-finals of another $10,000 ITF, this one in Nottingham. She did not pass the second round in any other ITF tournaments that season and finished the year with a ranking of world No.383.
In April 2008, Fitzpatrick reached her first ITF quarterfinal of the year in Toluca, a $10,000 tournament. Just two weeks later she reached her second of the year, this one in Irapuato $25,000. In June, the first of four consecutive wild cards allowed her direct entry into the main draw of the $50,000 ITF event in Surbiton where she lost to Georgie Stoop in round one. Her second wild card of June entered her into the main draw of the DFS Classic, a tier III tournament. She was beaten by Melanie South, 4–6 4–6, in round one. Wild card number three allowed her access into the qualifying draw of the International Women's Open where world No.62, Ekaterina Makarova, beat her in straight sets, 6–7(4) 3–6. Her fourth of four consecutive wild cards gave her entry into the qualifying draw of Wimbledon where she was beaten by Yuliana Fedak from Ukraine. In early August, Anna injured her foot while playing in an ITF in Portugal. The injury turned out to be a stress fracture in her left foot and it put her out of action for the rest of the season and as a result, she ended the season ranked world No.424.
Fitzpatrick returned to the ITF circuit in March 2009. In her very first tournament since injuring her foot, Anna partnered Stefania Boffa to win the title at the $10,000 ITF in Bath. She and Boffa again joined forced in Anna's next tournament, the $25,000 ITF in Jersey, where they reached the semi-finals. She made her first real impact in singles in July when she reached a $10,000 ITF quarterfinal before immediately going on to reach the final of another $10,000 ITF. She beat the fourth, fifth and sixth seeds before losing to Heather Watson, 6–4 4–6 2–6, in the final. In August, Anna played her final tournament of 2009 (a $10,000 ITF in London) where she was beaten by compatriot, Jocelyn Rae, in the semi-finals. During this tournament, her foot injury worsened once again and forced her out until March/April 2010. As a result of this, Anna's year-end singles ranking for 2009 was world No.761.