The former Labour Prime Minister said the statistics, compiled from previously unpublished data, show nearly 45,000 Scots now get help every year from the NHS in England, Wales and Northern Ireland.
According to information on organ donations from NHS Blood and Transport, and figures from the Scottish National Blood Transfusion Service, an average of 200 at risk Scots secure transplants from English or Welsh donors and a further 1,000 benefit from transfusions of blood donated in England, Wales and Northern Ireland.
A further 43,500 Scots receive NHS in-patient or outpatient treatments in the rest of the UK every year.
Publishing the figures, Brown, MP for Kirkcaldy and Cowdenbeath, said the details were evidence of the value of nations working together: "It makes the SNP's proposal to break all constitutional links with the rest of the UK out of sync with our more interdependent world," he said.
"Simply to chart those links and see the willingness to help each other in times of trouble should leave all of us bursting with pride at what we have achieved by working together. None of this must be put at risk."
However, a Scottish Government spokeswoman said the agencies involved had confirmed independence would pose no threat to such arrangements. She added: "The NHS in Scotland is already fully devolved and independence will not change the arrangements that exist between Scotland and the other parts of the UK in relation to organ donation.
"NHS Blood and Transplant, which co-ordinates organ donation across the UK, has already confirmed in writing that independence would not lead to any change in these arrangements.
"It is in the best interests of all patients across the UK to continue to share organs, to ensure the best match to recipient. This reflects international experience, and is also reflected in the fact that arrangements exist between NHS Blood and Transplant and the Health Service of the Republic of Ireland."