Most organic compounds are degraded or strongly bound to organic matter in soil, making it unavailable to plants. Even heavy metals, which plants sometimes take up because plants WILL take up metals, don't usually get taken up by the plants for those reasons. Just because toxic plant roots are nearby, it doesn't mean that the vegetable plants will take in any possible toxins. Plants are programmed to do what they do, and stuff in the soil that can't be used by that plant won't be taken in by the roots or used by the plant. Let's use the tomato plant as an example of how close the toxic and non-toxic plant parts can be. Tomato plants are genetically programmed to have toxic leaves, but on the same plant--on the same branch--we get non-toxic and nutritious tomato fruit.  The veggies growing in under your English Laurel should be fine.  Incidentally--carrots really don't pick up the "spice" from nearby radishes  :-)