I followed the very handy instructions at https://code.tutsplus.com/tutorials/quick-tip-how-to-work-with-github-and-multiple-accounts–net-22574 to set up different keys for my two github accounts.

My .ssh/config file looked like this:

Host github-work
    HostName github.com
    PreferredAuthentications publickey
    IdentityFile ~/.ssh/id_work

Host github.com
    HostName github.com
    PreferredAuthentications publickey
    IdentityFile ~/.ssh/id_rsa

I then had no problem cloning from github using `github-work` as a host

git clone git@github-work:work/work-project.git
Cloning into 'work-project'...
remote: Counting objects: 16, done.
remote: Compressing objects: 100% (12/12), done.
remote: Total 16 (delta 0), reused 16 (delta 0), pack-reused 0
Receiving objects: 100% (16/16), done.
Checking connectivity... done.

HOWEVER, pushing was another matter:

 git push -u origin master 
ERROR: Permission to work/work-project.git denied to mypersonalusername.
fatal: Could not read from remote repository.

Please make sure you have the correct access rights
and the repository exists.

The push was not using the right ssh key – the access denied message refers to my personal github account username.

For debugging purposes, I ran the following:

ssh -v git@github-work

Amongst the output was:

debug1: Reading configuration data /home/me/.ssh/config
debug1: /home/me/.ssh/config line 1: Applying options for github-work
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug1: Hostname has changed; re-reading configuration
debug1: Reading configuration data /home/me/.ssh/config
debug1: /home/me/.ssh/config line 8: Applying options for github.com

A bit of googling led to this stackoverflow post: why git push can not choose the right ssh key?.

The answer is to remove the vanilla/default github.com entry from the .ssh/config file so it only contains the section for the non-standard host. This works!