The Probate Service for England and Wales has added a searchable database for post-1995 wills and grants of probate. The database currently includes wills proved until well into 2014.
There is are two search options – simple or "advanced". With either type of search both the surname and the year of death have to be specified. So if you do not know when the person died or if you are trawling for a one-name study, you have to search separately for each year of interest. I have used the feedback button to suggest that the "year of death" become an optional field – you may wish to do so too.
If an entry is found, you can access a full copy of the document for £10. Payment entitles you to access the wills for 31 days. But you may not experience instant gratification, as the site warns that "you may have to wait up to 10 days for some documents".