Thank you very much! The solution seems to be http tunnel. What it does: there will be three proxy servers. The first one is to be installed on the local computer, it makes all connections to be going to a certain remote host on port 80. The second proxy server is on my LAN, which permits such connections. Finally, the remote host acts as a third proxy server and forwards the connections to the actual destinations.

The remote proxy server has to be provided and there is one such service available:
http://www.your-freedom.net/
I will try it and will let you know. It is probably going to be very slow, but anyway...