You may be able to get benefit for a period before you made a claim, but this depends on the circumstances. In some cases, you have to have a good reason for making a late claim and in other cases, the reason does not matter.
The deadline for backdating a claim depends on the benefit. For example, you can get backdated Housing Benefit for six months if you can show you have a good reason for not claiming earlier (for example, you were given the wrong advice).
You also have to show that you were entitled to Housing Benefit throughout the period of backdating – i.e. that you were paying rent, and your income was low enough. You will not usually get any backdated benefit just because you did not know that you could make a claim.