make a base for the cardboard tube out of a similar weight piece of cardboard, or a margerin tub/icecream tub etc...tape the base in place inside the tube.
Then dilute some PVA glue until it is still sticky (so not as dilute as papermache paste, but easy to paint with ) and paint the bottom inch or so of the container. Now, take some ordinary string or twin, natural colour variety; and carefully coil the string round the tube fitting it tightly so that you can't see the tube through the string. Paint the string with PVA glue also. Gradually work you way all the way up until the entire tube is covered.
Once dry you can use to hold dried flowers, or line with a clear plastic bag and use for fresh flowers. Depending on the size of the tubes, yo will have to cut them to size as appropriate.
As a variation, you can do exactly the same, but cut the tube to just a few inches long. Then make a lid for the tube from a piece of card and coil the string, flat around the lide and use as a small box for gift presentation.