My installation has seemed to go OK on a typical shared server (UK2.net)
The installation checks all passed fine, the post-installation screen showed the locations of all actions
The database has been created.
But I cannot log in with the admin name and password.
I checked the database no users are logged
I can access the Management.php page but log out and then cannot log in again
That is expected behaviour. You can only login on the management.php page with the admin login. If you selected Db as the authentication method (which I think you did) then you first need to add users in the Users tab of the management.php page. If you do not have a User tab, please set the Authentication method to Db first (in the Site->Authentication section of the management.php page.