Keyboard navigation to Hyperlinks

I'm creating a course and I need to ensure it's as accessible as possible.

I've got one page with a number of hyperlinks out to external websites, each link in a separate text container.

When using the mouse they work fine, but when I try to open the links using the keyboard (space or return), selecting a single link opens every link that's on the page.

Any idea why this is happening and what I can do to stop it from happening?

Thanks