British Irish Visa Scheme:

Indian citizens can apply for one travel permit to visit both the UK and Ireland through British-Irish Visa Scheme (BIVS) in India. As per BIVS, applicants should apply for the visa of the country they wish to visit first. If you have an Irish short stay visa and you also want to visit the United Kingdom you must travel to Ireland first. If you have a British short stay visa and you also want to visit Ireland you must travel to the United Kingdom first. The BIVS issued visas will have BIVS coding endorsed on it.