The Government is resuming pension and benefit payments to thousands of people with bank accounts in Cyprus and with affected Cypriot banks in Greece.
But the Department for Work and Pensions (DWP) also warned that it could be next week before the money shows up in many people's accounts due to backlogs in the banking system.
The freeze on benefit payments into Cypriot bank accounts was announced on March 18, while Cypriot politicians hammered out plans for a levy on accounts under a European rescue package to save the country from bankruptcy.
The UK Government, which has been encouraging people to use a British account, previously said the aim of the freeze was to ensure that payments reached their intended recipients.
Around 18,000 expats living in Cyprus receive a British state pension, but around one third of these use a British bank account and so were not affected by the freeze. There have been reports of some pensioners struggling to cope and clubbing together to buy food parcels.
The DWP said on its website that, now that banks in Cyprus have reopened, it is processing payments. But its statement also said: "Customers are likely to find that it takes a number of days - and probably into next week - for these to be credited to their accounts, due to backlogs in the banking system."
The Government said it is continuing to monitor the position in Cyprus from both London and Nicosia. It said that anyone who wants to find out more information should contact their local bank branch or the International Pension Centre - https://www.gov.uk/international-pension-centre.
On Tuesday, it emerged that around 15,000 savers in the UK arm of stricken Cypriot bank Laiki will see their deposits protected under British rules and will escape any banking levy.
New City watchdog the Prudential Regulation Authority said around £270 million in deposits from Laiki Bank UK had been transferred to Bank of Cyprus UK and would come under the UK compensation scheme, guaranteeing up to £85,000 per saver.
Customers, including those with current accounts in credit, will not be hit by any Cypriot levy on their accounts and will be able to access them as normal.