Can I install Mojave on boot drive and still keep Catalina running I’ve tried a few times now but I get a message ‘you need to update to a later os’ when I try to boot up from the external.

It would seem that Catalina doesn’t like it. I still want Catalina installed but I need Mojave as an external boot drive.

Any ideas anyone?
I have a new MacBook Pro running Catalina.

macs require you to run whatever macOS was shipped with the machine or a latter macOS.  So, you bought a new mac that came pre-installed with Catalina which means you cannot run Mojave on it.  You could get a virtual machine and run Mojave in the virtual machine.  You can get Parallels and run Mojave.  You can try the free virtual box, but expect some difficulties install macos.

If you are still in the free return period, you can return your machine. Look for a new machine with mojave on it.