I suspect the router in my network prevents the block chain from being sucked into my machine, using the classic way, i.e. bitcoin-qt or bitcoind.

You should check if you can open the 18333 and 18332 port on your router.

Is there a way of dowloading the testnet block chain?

I havent find a direct link to download it but you could do it yourself:

1. Find a separate computer which share the same operating system and is able to download the blockchain.
2. download the whole blockchain repository which size is ~2GB
3. Copy the repository of the blockchain which location depend on your operating system mine is in /home/user/.bitcoin/testnet3 then put it on a usb drive for example.
4. Then go back to your first computer and put it on the same repository as your first computer.