There are two main criteria which you must first satisfy to immigrate to the U.K. from Ireland. To gain "ight of residence you must either be working in the U.K. or be able to support yourself and your family financially without becoming an unreasonable burden on public funds.
For example, you cannot immigrate to the U.K. from Ireland and start collecting welfare benefits immediately; this will ultimately result in deportation back to Ireland.
If you satisfy one of these two criteria, you will gain right of residence in the U.K..
You will also require a valid Irish passport to physically travel between Ireland and the U.K..
Once you have gained the right of residence in the U.K., you can also move your family to live with you.
Your family includes your spouse/civil partner, any children or grandchildren of you, your spouse/civil partner. However, the children must be under the age of 21 or dependent on you. This also includes your grandparents or those of your spouse/civil partner.
Other family members can reside with you, but they have to prove they are dependent upon you. If you are not married or in a civil partnership, you must be able to prove that you are in a committed and lasting relationship.
If you have family members who wish to live with you in the U.K. but are not from an EEA member country or Switzerland, they are required to apply for an EEA family permit. This permit and it's application process is similar to that of applying for a visa.
Family permits can be applied for at any British diplomatic center, such as your nearest British embassy.
Visit fco.gov.uk to search for your nearest embassy.