I always avoid that option. Many, but not all, items on Amazon offer free postage anyway, with the only difference to the 'Prime' offering being that you don't get automatic next-day delivery.
Click the option to continue without Prime and then take a look at the delivery options available to you. (NB: If free delivery, without Prime, is available, it won't be pre-selected for you. Refusing the Prime offer gets you to a screen where the regular postage for next-day delivery has been added on. You need to look to the right of that to find the option to select free postage with a slightly slower delivery time - although, in my experience, it always gets to you really fast anyway!)