It depends! The clay is not the problem, Laurel loves a nice bit of clay.

The problem might be too much water & damp.
In our part of the world, evergreen trees generally shun wet soils.

Clay will tend to trap water if it can, but it all depends on where you are planting it.
Clay on a hill top will be perfect, but clay at the bottom of a sloping garden with a wall at the end in a low valley where it rains all the time is likely to be pretty bog-like (unless it has had proper drainage works installed – so many possibilities!).

The bottom line is this: if puddles persist on the surface of the soil for over 12-24 hours after a period of heavy winter rain, your soil is on the wet side and Laurel is not the best choice.

Holly, Ilex aquifolium, is a native tree that is much happier in our climate. If you have concerns about the drainage in your site, it is worth considering it.

I hope that helps!