Paloma, a Category Four storm with winds approaching 140 mph, hit the Cayman Islands on 8 November, causing serious flooding and other damage.
The British Red Cross donation, from the organisation's Disaster Fund, will be spent on tarpaulins to help give temporary shelter for those whose homes have been damaged by the storms, as well as food and water for people in hurricane shelters.
In the run-up to the hurricane hitting, the Red Cross pre-positioned supplies and volunteers around the islands and opened shelters. National shelters have also been opened.
The Cayman Islands have experienced non-stop rain for two weeks and there was much localised flooding even before the storm hit. Poorer communities in the south-west of Grand Cayman are especially at risk, as their housing is less stable and more likely to sustain serious damage.
Already hit by Hurricane Gustav in September, the Cayman Islands have not yet been able to fully replenish relief supplies expended during the earlier storm.
The local branch of the Red Cross was also helping tourists trying to leave the islands ahead of the hurricane.