I suspect that the turf you laid wasn't specifically for shade - which is why it hasn't grown.

There is a grass seed especially for shaded areas, but I'm afraid I don't know of any turf for the purpose.

the other thing is the trees arnt just cutting out the light . they will take a supstantial amount of the goodness out of the ground beneath them to .

Grass is a plant, so needs lots of water and light. You can get grass varieties that tolerate shade more than others, but that turf is very expensive (say £8-10) per metre against regular turf which is about £3 per metre.

Trees will have shallow roots, so you need to train them to go down to stop them stealing your grasses water. So you need to really water the area near the trees heavily but infrequently - say every Saturday on a heavy sprinkler for 1-2 hours.

Between the two you should get a decent lawn eventually.