Notafish - Allergies and the bodies immune response is a complicated thing, not easily explainable in one of these texts :)
Suffice to say - The most serious allergic response is the IgE- mediatated immune response, which is the one that causes the immediate, dangerous response. Non-IgE mediated responses can also occur, but they tend to take place some hours after the supposed exposure.
Now, what the York Test Laboratories offer is a blood test which looks for IgG antibodies - but these do not typically cause an immune response such as allergy or "intolerance" - quite the opposite actually, IgG antibodies only indicated exposure to a particular component within a food. An IgG marker does not indicate a food intolerance or an allergy.
It is difficult to test for the true allergic response - the IgG mediated response, because it is so rapid acting, and it can often be difficult to obtain a blood test when such a reaction occurs - so an IgE test, unless blood has been taken during the response, is fairly useless.
A proper analysis of allergy or intolerance is, I am sorry to say, much more laborious than a blood test - requiring controlled exposure to particular reactants, coupled with observation, blood tests etc.
If you have an interest in the science behind all of this, take a look at the following link - very good overview of the different tests available, and why an IgG test is not really all that useful.
http://www.sciencebasedmedicine.org/index.php/igg-food-intolerance-tests-what-does-the-science-say/