One of the purses, containing a small quantity of cash and some credit and bank cards, was stolen from a walking trolley in the British Heart Foundation shop between 3.30 and 4pm.
Another purse was taken, sometime before 4.30pm, from a handbag in the Cancer Research shop. It contained a small quantity of cash and a credit card.
Police said no suspects were seen.
Anyone with information is asked to contact Sussex police via email email@example.com or by calling 101, quoting reference 47160073611 of 01/6.
Police remind all shoppers to remain alert and aware of their surroundings at all times, and to take good care of their bags and other property.