No, they are not the same.
Washing soda is Sodium Carbonate. The domestic product is an impure or "technical" grade of sodium carbonate and comes in the form of very large white crystals.
You should be able to find washing soda in most corner shops such as Spar etc. I called in a Co-Op branch on my way home from work last night and it was on the bottom shelf in the household section. Tesco, Asda stock it around the same place. It's sold in boxes of 1Kg which look like small washing powder boxes.
Sodium Hydroxide is extremely caustic and is not something I'd recommend for use in washing machines as it will damage the washing machine because of it's corrosive properties.