Our meds consisted of a Q&A with doctor (family history, heart conditions, mental health, how much do you drink/smoke that sort of thing). You have to do bloods and urine but, if you have a fairly clean medical record, you should be OK. You also have to have X-rays to check for TB. They are really just looking for any long term serious conditions that, as someone mentions previously, could be considered a long term drain on health resources. Minor onditions, or anything controllable with OTC drugs should not be a problem. You may also to check whether your vaccinations are up to date, Hepatitis B, Tetanus and a couple of others.
Kids under 5 should not need bloods, babies should not need to give a urine sample.
Lee