During the Olympics we allowed people to work from home. One has requested to work from home full time since then. Do I have to agree if they say it worked okay during the Olympics?
No not necessarily, but you need to follow the correct procedure outlined in the flexible working regulations.
If you refuse the request it must be for one of the prescribed grounds: burden of additional costs; a detrimental effect on ability to meet customer demand; an inability to reorganise work among existing staff or recruit additional staff; a detrimental impact on quality or performance; insufficiency of work during the periods the employee proposes to work; and planned structural changes.
But do bear in mind that sometimes a refusal of flexible working can sometimes be discriminatory.