This is sort of a ‘how long is a piece of string?’ question.
It all depends on the lender. An application can take anything from a few minutes or a day, to several weeks.
Where they differ is the process after the application. For instance, a small personal unsecured loan is likely to be faster than a mortgage for £200,000, as additional documentation is required.
So the piece of string really depends on your situation, the lender you choose, the forms to complete, and how quickly you can return the forms.