I am proud owner of two “beebs” with several extensions.
I was also interested in playing some games, so I looked for a joystick adapter. What I found was not really satifying. None of them were properly switching to ground, which means you can’t use any joystick with active functions, like auto-fire.
I really wondered why people did this, as it is not so much of a difference to do it properly in the first place. So I designed a new one. “Ground is ground” on both sides, the BBC-B connector and the two Atari-type ports. And both can be supplied by the BBC-B with +5V for active functions available in the Joystick.
I am not a commercial distributor and my projects are just for fun. But I have a few PCBs left I am willing to give away, in case you are interested.