When my niece was suspected to have lactose intolerance they took her to the GP, and to be honest I don't think they suspected lactose intolerance at this point, just illness, but she was tested by either the nurse or the doctor at the GP and then sent to a dietitian. I'm afraid I don't talk to my sister that much so I can't realy give you anything more than that.

But! I do also know that a friend of mine thought she had a milk allergy and last time I spoke to her she was planning on getting it tested on the NHS, so you can be tested for it, but I wouldn't know exactly how you would go about getting the test.