I didn't want to post a new answer but instead make a comment, but alas, not enough reputation.

I just wanted to add to Daemon Painter's answer and say that the final total bill also isn't working as it is multiplying a dict by an int.

What could work is to initialize out of the loop the total variable as well a new total_cost variable, and place:

total_cost += total

Inside the while loop but outside the if conditions. That way the last line can just be:

print("The total price of your basket is: ", total_cost)

Edit: the code, working as intended:

    price = {"Lemonade": 1.50, "Coke": 2.00, "Fanta": 1.00, "Water": 0.50}
    shopping_basket = {}

    print("Welcome to the online drink store!\nThese are the drinks we offer\n1. Lemonade: £1.50\n2. Coke: £2.00\n3. Fanta £1.00\n4. Water: £0.50")

    buy_another_flag = 1
    total_cost, total = 0, 0

    while buy_another_flag != 0:
        option = int(input("Which drink would you like to purchase?: "))

        if option == 1:
            qnty = int(input("Enter the quantity: "))
            total = qnty * 1.50
            print("The price is: " + str(total))
        elif option == 2:
            qnty = int(input("Enter the quantity: "))
            total = qnty * 2.00
            print("The price is: " + str(total))
        elif option == 3:
            qnty = int(input("Enter the quantity: "))
            total = qnty * 1.00
            print("The price is: " + str(total))
        elif option == 4:
            qnty = int(input("Enter the quantity: "))
            total = qnty * 0.50
            print("The price is: " + str(total))

        total_cost += total

        buy_another_flag = int(input("Would you like another item? enter Yes (1) or No (0):"))
    print("The total price of your basket is: ", total_cost)