This depends on the specific lease conditions and who owns the freehold.
Staircasing a flat to 100%
When you staircase a flat to 100%, the freehold won't be transferred into your name.
Staircasing a house to 100%
When you staircase a house to 100%, then you may be able to transfer the freehold into your name; however, this isn't automatically done, and it may not actually be transferrable.
The housing association may only own the leasehold for your property, while the freehold is held in another party's name. In the staircasing process, the housing association is only able to staircase the lease they own and can't agree to transfer the freehold to you if they don't own it.
You should find out who owns the freehold. If the housing association owns the freehold then agree with them to transfer this into your name when staircasing to 10%. If the freehold is in another party's name then contact them and find out if they will agree to transfer the freehold into your name. They will often want to be paid a premium to do so and you'll often have to pay for their legal fees to do so.
A freeholder no longer has to pay ground rent, however small this might be). This is not always the case, however, and sometimes there may be a stipulated time period - for example, 3 months - before the freehold title passes to you: your solicitor will advise you further about this.
If you're changing ownership from leasehold to freehold, then you'll have to arrange your own buildings insurance. Quite often, your lease will contain a clause which forces you, if you sell up within 3 months of full staircasing, to give the housing association any difference between the price your home is sold for and the amount determined by the open market valuation. You can normally remove this clause after 3 months.