David James Taylor, 33, and his Australian girlfriend Sara Connor, 45, have been detained over the death of Wayan Sudarsa.
The policeman's body was discovered at Kuta beach at 03:30 on 17 August with dozens of head and neck wounds.
The pair face up to 15 years in jail if they are found guilty of murder.
Mr Taylor's lawyer, Erick Sihombing, said his client confessed to hitting the the police officer after accusing him of stealing Ms Connor's missing handbag.
"He found an old cell phone, he hit the guy's head on the back maybe twice. There is a bottle and an old phone," Mr Sihombing told the Australian Broadcasting Corp.
"They found on their clothes and trousers a stain of blood and hair, that's why they tried to get rid of them by burning their clothes."
The couple were apprehended by police outside the Australian Consulate in Bali on 19 August.
Mr Taylor - who performs as DJ Nutzo - is originally from Halifax had reportedly been dating Ms Connor for three months.
Police said the couple's blood was found near the crime scene, in their hotel room and on Mr Taylor's scooter.
Authorities said a broken beer bottle found near the crime scene may be the murder weapon.
The pair have been named as suspects in the murder but under Indonesian law have not been formally charged.
Police have 120 days to build their case before prosecutors decide if they will lay charges.
Both are receiving consular assistance from their respective countries.
Ms Connor had reportedly gone to Bali to meet Mr Taylor after he was unable to get a tourist visa for Australia.
The mother-of-two is well known on the New South Wales north coast for her small business Byron Bay Fresh Pasta.
Ms Connor's legal team insisted she was not involved in the killing.
On 21 August her family issued a statement in her defence: "The accusations laid against her are totally out of character."
Bali is a popular Western tourist destination, known for its tropical climate and palm-fringed beaches. Petty crime is common on the island, though more serious crime is rare.
A British man has reportedly admitted he had a violent confrontation with a police officer on the Indonesian resort island of Bali.