I want to leave my property earlier then the end of the contract. Can I have my deposit back?

This is a question for your landlord or their agent.

I live in england. My tenancy is 12 months. If I leave on the 10 month the landlord can keep the deposit or is not aloud?

Generally when you break your lease, you are still required to pay rental until the end of the lease or until the landlord re-lets the unit. If you want to leave early you need to get the landlord's agreement. Usually the landlord may offer you a buyout of 2+ months rent.

If you leave early without permission than the landlord can hold your deposit towards unpaid rent.

My tenancy finish the 31 of July, and we want to live the 5 of June. I'm going to send the month notice the 5 of may. What can happen then? I always paid the rent in time and they have my deposit

They can demand the money for the last two months where you don't pay. You can give notice, but they don't have to accept it, they can merely let you move but expect you to keep paying the rent. So I assume you don't plan on just talking to them and asking them first ?