This is possible, but you will have to complete the sale of your own house, to release money to pay the 10% deposit before you sign contracts for the new house. This means moving out to temporary accomodation for a while.
If you can't manage this, then there are alternatives, but they will cost.
You obviously have equity in your current house, so talk to your lender about the possibility of releasing some of it to pay the deposit, so you dont have to complete the sale. This will cost you in extra interest and remortgaging costs.
THe stamp duty is OK, because it is payable on the day you complete the sale, so if you complete both transactions on the same day, your solicitor will take the stamp duty from the sale cheque.