I think I've lost all my photos on machine that died

if your OLD iPhoto library did not get restored with the rest of your backup data, you may need to ask Time Machine.app (not to be confused with Time machine control panel) to restore it manually.

navigate to the folder on your current Mac that should contain your photo library.

if the old iPhoto library has NOT been restored there, launch Time machine app. you get the Star Wars display, featuring the current view of that folder, with older versions stacked behind it, receding back in time:

specify the version you want, by using scroll bar on the right or by clicking through older versions until you get the folder contents you wish to have available.

Then click on restore and follow the directions.

Restore items backed up with Time Machine on Mac - Apple Support

Once you have the file(s), you still may have to import into the current version of Photos.

Can you explain the situation more clearly?

You did Time Machine backups of your old (failed) Mac. Have you used that backup drive for anything since getting the new Mac?

When you set up your new Mac, on first boot up did you specify the TM backup drive and "migrate" your account and files from it?

If not, how did you set up your new Mac? If you did not "migrate" from the backup drive, did you create a new user on the new Mac with the same name as the user on the old Mac?

Anyway, I have been trying to access my photos which were in downloads from my Time Machine. I have managed to find the old machine's back-ups but I can't access the downloads I had saved on it

What do you mean by "downloads?" And what do you mean by "I can't access the downloads?" What exactly happens or what do you see when you try?

P.S. I don't think you have lost all your photos. But it may take a little effort to retrieve them.

DO NOT go digging in Time machine backups use the Finder.

Time Machine creates a complex database, built from dozens of snippets from the initial full backup and all the incremental backups.

navigate to the folder on your current Mac that should contain your photo library.

if the old iPhoto library has already been restored there, all you need to do is tell new Photos to Import those photos:

Import photos from another library in Photos on Mac - Apple Support