You may have left it too late for anywhere particularly special on Corsica as it's heaving with French and Italians .............. but it is very beautiful - I spent a long week touring 2 years ago in May and it was spectacular (but slow driving in the mountaineous interior).
Turkey will be cheaper, hotter and probably will have more availability. Although the distance from the UK is further in terms of air travel, it is less expensive!! Without wishing to sound prejudiced, I think you will find that Turkey is more flexible in its ability to welcome UK visitors than Corsica.