This page has audio clips and videos that people who are using a Tilbury whistle have sent to me. You can get an idea of how it sounds from these.
This is a recording of P.J. TinWhistler playing Drowsy Maggie, The Cat's Meow, Farewell to Whalley Range. You can subscribe to his youtube here.
Here is another recording of P.J. recording some Galacian and Breton tunes. You can subscribe to his facebook here. Names of the tunes: Muiñeira de Chantada (Galician) / An Cailín Deas Crúite na mBó (The Pretty Girl Milking Her Cow) / Ridée 6 Temps (Breton).
Here is a video from Richard Williams. It's called Boolavogue. Very nice.