Look at a size chart to find your U.K. sizing. Irish dance shoes may only be listed in U.K. sizing.
Put on a pair of poodle socks before you go try on shoes. Find a store in your area that sells dance shoes. Find the correct type of shoe for the type of Irish dance that you do. Irish step dancing requires hard soles. If they do not have Irish dance shoes, try on a pair of jazz shoes, which are similar. Try doing some dance steps to see if they pinch or slide.
Make sure the return policy is acceptable. If the shoes do not fit, you should be able to exchange them.
Order the shoes if you are buying them online. Make sure the company accepts your form of currency if the shoes come from Ireland.