I see in >System>DB Management (admin/admin_dump.php)
there is a link on the page: "Create new dump"
 
I have read the section on backing up the database with MySQL but it would so much more convenient to be able to back up from inside my site admin each day.
 
I assume that this link will create a backup to my local disk ?
As I cannot find a mention in the manual I would be pleased to get re-assurances just in case it actually overwrites tables

No, it will be in the host's HOME/db fold.
 
Then you can FTP to your local if desired.

"Create new dump" will create a dump file in your site's /db folder. It does not send it down to your local disk. You would need to use FTP to get a copy of it.
 
When you select "Create new dump", you are presented with another screen where you specify ...
 
Dump filename - dump file name
 
Create a table structure (or data only) - to include statements to recreate the tables
 
Available Tables - Select the tables you want to backup (or dump into the file) and select "add" to add to the list on the right.
 
This process does not overwrite tables. However, if you select "Apply Dump" next to the filename listed on the "DB Management" screen, it will overwrite your tables whether you specified 'table structure' or not when you dumped it because within the sql file is a statement that deletes all the records of that table before inserting the records back in.