You have two options here.

The Queue-Mode configuration option

The default, "host", creates one outgoing connection for each host. If you set it to "access" it will create one connection per URI type (which I understand to mean, one for http, one for ftp, and so on - since most connections are http, this means it'll access each server sequentially).

One way to do this that will also apply to update-manager is to:

echo 'Acquire::Queue-Mode "access";' >/etc/apt/apt.conf.d/75download

if you want to try it with apt-get once to see if it helps:

apt-get -o Acquire::Queue-mode=access update

The Acquire::http::Dl-Limit option

This is similarly to reduce the bandwidth used to something your connection can handle (and as per the manpage, "this option implicit deactivates the download from multiple servers at the same time").

echo 'Acquire::http::Dl-Limit "70";' >/etc/apt/apt.conf.d/75download

or

apt-get -o Acquire::http::Dl-Limit=70 update