Without FTP access, if you have an administrative login to the WordPress admin you can grab the code from plugins and themes one file at at time.
For themes go to Appearance > Editor
For plugins go to Plugins > Editor
Select the appropriate theme / plugin and go through the list of files downloading the code, css, etc.
This will not have the images, but you should be able to reconstruct the plugins and themes from this and what is publicly available to download using a website scraping tool… albeit a tedious process.
The best option would be to convince the current host to provide FTP access.