If it's totally in the shade maybe try a gravel garden, or if it gets some sun you can buy grass seed that is especially for shady areas from garden centres.

Is there anything you can do to reduce the amount of shade? And is the shade all over the garden, all the time, or does some sun get there sometimes?
How big is your garden anyway?

What makes you say the garden gets 'ruined by worms' all worms do it tunnel through the soil and pop up occasionally - the do not ruin the soil!

Wormcasts are a GOOD sign, Foords. Worms are a garden's best friends. If the casts look unsightly, wait until they dry and just brush them back into the lawn. We used to have a north-facing garden, and for virtually the whole day, year round, the lawn was in shadow. We got lots of moss in it, so we decided NOT to use "Weed and Feed with mosskiller" on it each spring, but to rejoice in the greenness of anything that would grow. It's called "making a virtue of necessity", and the moss was a brilliant and beautiful green. Yes, Crv1963 is right, you can get special seed for shaded lawns, but I don't know how good or effective they are. Worth a try?

I agree with Gattina. We like our moss lawn. The birds do too.