She began her international junior career in cross country running in 2001, highlighted by 33rd place at the 2003 IAAF World Cross Country Championships. She won a steeplechase silver at the 2006 European Cup and also competed in the event at the European Athletics Championships, being eliminated in the heats. She took the under-23 silver medal at the 2006 European Cross Country Championships at the end of the year. She was fourteenth in the senior race at the 2007 IAAF World Cross Country Championships – the second best European performer behind Jessica Augusto (12th). She made her global track debut at the 2007 World Championships in Athletics and was twelfth in the steeplechase final. She ended the year with a seventh-place finish at the 2007 European Cross Country Championships.
She made her Olympic debut at the 2008 Summer Games in Beijing, but did not make the women's steeplechase final. She came eleventh at the 2009 European Cross Country Championships which was held in her home city of Dublin. Britton was also eleventh in the steeplechase final at the 2010 European Athletics Championships. She just missed out on a medal at the 2010 European Cross Country Championships, finishing with the same time as bronze medallist Ana Dulce Félix. She took second place at the Lotto Cross Cup Brussels a week later.
In preparation for the world competition, she ran at the Almond Blossom Cross Country in March 2011 and took second place. She managed 16th place at the 2011 IAAF World Cross Country Championships in Punta Umbría. She ran a personal best of 15:31.26 minutes for the 5000 metres at the FBK Games in June then ran a steeplechase best of 9:37.60 minutes at the Adidas Grand Prix in New York. Britton represented Ireland on the track at the 2011 World Championships in Athletics, narrowly being eliminated in the first stage of the steeplechase. In November she came third at the high-level Cross de l'Acier cross country race. In December 2011, she won the gold medal at the 2011 European Cross Country Championships.
She began 2012 with wins at the Great Edinburgh Cross Country and Antrim Cross Country. She expressed her disappointment that the World Cross Country would not be held that year, and stated that she would focus on track running that year instead. In December of that year she became the first woman to defend the continental cross title claiming victory at the 2012 European Cross Country Championships.