The British Government is sending staff from the consulate in Bali and embassy in capital Jakarta to assist stranded British tourists.
A spokesman for the Foreign and Commonwealth Office (FCO) said: "We are working with the Indonesian authorities to provide assistance to British people caught up in the earthquake in Lombok and the Gili islands.
"FCO consular staff are deploying to Lombok to provide assistance to those who need it.
"Bali and Lombok airports are open and running a full service. Extra flights are being added to help people who wish to leave Lombok.
"Anyone travelling to the area should check the latest FCO travel advice which is being regularly updated."
The Red Cross is providing blankets, sleeping mats, water and other provisions for those caught up in the devastation.
Ben Webster, head of emergencies at the British Red Cross, said: "The top priority now is reaching people affected by the earthquake and subsequent aftershocks.
"The Indonesian Red Cross is still hearing reports of villages in remote areas cut off without any help. They will need food, water, clothing and temporary shelters.
"The Red Cross is doing everything it can to reach them and continues to distribute blankets, tarpaulin, sleeping mats, water, as well as providing healthcare and other support, to those that have been affected."