The scheme stepped in to protect members of Kensington & Chelsea Credit Union Limited (known as K&C and also trading as ‘Your Money’), which has stopped trading and is now in default.
This means the credit union cannot repay deposits to its 1,100 members.
FSCS says it aims to compensate the vast majority of members within seven days.
Using the credit union’s records, FSCS will send payments out automatically.
Members with up to £1,000 in their account will receive a letter to get cash over the counter at their local Post Office.
Anyone with more than a balance of £1,000 will receive a cheque for their balance direct from FSCS.
FSCS protects up to £85,000 of savings – double that for joint accounts and has come to the aid of more than 4.5 million people since 2001, while paying out over £26bn in compensation.
FSCS expects the total pay-out for Kensington & Chelsea Credit Union Limited members to be £1.1m.
Alex Kuczynski, chief corporate affairs officer at FSCS, said: “Everyone wants to know their money is secure, but they might not know about the safeguards in place.
“FSCS is here to protect members of Kensington & Chelsea Credit Union Limited and get them back on track.
“Their savings are protected up to £85,000 and joint accounts are covered for £170,000.
“Our aim is for the vast majority of customers to get their money back within seven days.”