Officers from 26 forces and the Serious Organised Crime Agency (Soca) were involved in the operation.
Searches have taken place in London, Sussex, Cambridgeshire, the West Midlands, Essex and Northern Ireland.
The raids are in connection with the theft of Chinese artefacts and a rhinoceros horn in 2012.
Six burglaries took place over a four-month period, police said.
Three happened at Durham University's Oriental Museum, one at Gorringes Auction House in East Sussex and one each at Norwich Castle Museum and the Fitzwilliam Museum in Cambridge in April last year.
Although much of the stolen property was recovered, several high-value items are still missing.
So far, eight people have been convicted and jailed for a total of more than 40 years for their roles in the break-ins.
Hundreds of officers were involved in the raids early on Tuesday.
Five men - aged 20, 31, 35, 53 and 54 - and two women, aged 28 and 54, were arrested in London.
Four men - aged 24, 41, 44 and 56 - were arrested in Cottenham, Cambridgeshire, after police broke down the door of a mobile home at Smithy Fen travellers' site.
Two men, aged 28 and 46, were arrested in Basildon, Essex.
A 60-year-old man was arrested in Sussex, a 32-year-old man was arrested at an address in Walsall, and a 67-year-old man was arrested in Nottingham.
Three men have also been arrested in Northern Ireland.
All are being held on suspicion of conspiracy to commit burglary, apart from the 54-year-old woman who was arrested on suspicion of perverting the course of justice and assisting an offender.
They are currently in custody at police stations across England and Northern Ireland.
Searches are continuing at various locations.
Chief Constable Mick Creedon, the Association of Chief Police Officers' lead for serious organised crime, said: "The series of burglaries last year had a profound effect on museums and similar institutions and we are committed to bringing all those who were involved in the conspiracy to justice.
"Many of the stolen Chinese artefacts are still outstanding and a substantial reward remains on offer for information which leads to the safe return of those priceless items."
Police investigating thefts of "priceless items" from museums and auction houses in England have arrested 19 people in dawn raids.