If there were a totally official Ubuntu mirror that used HTTPS, that might be your best bet: unless you have configured your computer to recognize the proxy you're required to use as its own certificate authority (which would be insecure unless you totally trust the proxy and controversial anyway), the software that restricts what you may download cannot distinguish filenames by extension, through HTTPS.
Unfortunately, the current official mirrors for Ubuntu ISOs are http, ftp, and rsync only.
Fortunately, HTTP mirrors occasionally support HTTPS as well. By going through the list, you'll often find a small number that do. In particular, you can download Ubuntu ISO images from https://mirrors.kernel.org/ubuntu-releases/.
(The HTTP version of that site actually isn't listed--I got it by removing the "us" subdomain prefix from http://mirrors.us.kernel.org/ubuntu-releases/. The HTTPS version of that site should work too but you'll get scary warnings in your browser because its security certificate is for the unprefixed domain instead.)
Note that, once Ubuntu is installed, you may have some trouble updating it and installing software in it, depending on what extensions you can download via HTTP. In particular, you must be able to download
.deb files. Hopefully the block is limited to just a few extensions rather than blocking everything but just a few extensions.
You can also make Ubuntu use HTTPS download mirrors to update and install software, same as with HTTP. I don't know of any HTTPS sites mirroring Ubuntu's official software sources--those mirrors aren't, in general, all the same as the mirrors for ISO images--but if you need that, you could post a new question about it. (In your question you should explain why you need it, as otherwise it will likely be answered with an explanation of how APT operates securely even though archives are downloaded via HTTP.)