Feel a bit silly - a bit more googling turned up the answer I was after:

RedirectMatch ^/$ /git/

Basically redirecting the root, and only the root.

This code could do in a .htaccess file (there is a tag for this, so I assume that is the original use case). But if you can edit ,the main server apache config then put it in the section for your website probably inside a <VirtualHost> section.

The docs for RedirectMatch say that the context can be "server config, virtual host, directory, .htaccess".

Correct way in new versions of nginx

Turn out my first answer to this question was correct at certain time, but it turned into another pitfall - to stay up to date please check Taxing rewrite pitfalls

I have been corrected by many SE users, so the credit goes to them, but more importantly, here is the correct code:

server {
       listen         80;
       server_name    my.domain.com;
       return         301 https://$server_name$request_uri;
}

server {
       listen         443 ssl;
       server_name    my.domain.com;
       # add Strict-Transport-Security to prevent man in the middle attacks
       add_header Strict-Transport-Security "max-age=31536000" always; 

       [....]
}