Assuming you do not have a mortgage or other charge on the property, contact your nearest land registry and ask them for advice. You will need to complete form TR1.They really are very helpful:
If there is a mortgage on the property you will first have to transfer the mortgage to your partner, and the lender will want to be sure he or she can afford it. Fees will probably be incurred for this.
You also need to think very carefully about why you want to give your house away. You may have good reasons but on the face of it it's an irrational thing to do. Half, yes, but not the whole house.