[Edit] 29/1/22 Closed unfortunately. Another Thai cafe/restaurant opening in the old premises.
The closest you will get to Thai street food in Portsmouth is Noodels. Found in Edinburgh Rd, at the City Shops South Stop A, just around the corner from the Cascades Shopping Centre.
The beef noodles noodles are delicious
Self service, chilled water and condiments sets seldom seen in the UK.