Numerous questions have arisen regarding travel between the United Kingdom and the Republic of Ireland (ROIRepublic of Ireland). Since both countries are a part of the Common Travel Area (CTA), flights originating in ROIRepublic of Ireland bound for the UK and vice versa may not have Immigration Officers available to stamp passports of non-citizens upon arrival. This may not be an issue for visitors, particularly non-visa nationals, but for those who are on student visas, spousal visas, HSMP, Work Permit, etc it could prove to be problematic.
If you are entering the UK for the first time on a visa, you need to have a stamp showing when you first entered the UK. If you travel to the UK via the Republic of Ireland, it is advisable that you notify the flight crew before you board the plane to leave ROIRepublic of Ireland. They can try to arrange to have an Immigration Officer available at the destination. If this does not happen you should actively seek out an Immigration Officer at the destination airport. On occasion, you may not find anyone in the arrivals area. If that is the case, the course of action would be to send your passport along with evidence of arrival such as a boarding pass to Immigration. This includes those who fly to the Republic of Ireland and then travel by land into Northern Ireland since the border is open. Information regarding this is available for American citizens on the United States Consulate, Belfast website. http://london.usembassy.gov/nireland/niscs.html
It is also advisable for those who are already resident in the UK on FLRFurther Leave to Remain who visit the Republic of Ireland (via air travel) to ensure their passport is stamped. When applying for ILRIndefinite Leave to Remain, you are expected to have been in the UK for a certain period of time. If you can prove all exits from and arrivals to the UK, it will be easier for the Border and Immigration Agency to determine if you meet that time criteria.
It is important to note that only citizens of the Republic of Ireland, the United Kingdom and the Crown Dependencies can travel freely throughout the CTA. Even though there may not be officers checking passports upon arrival, it is the responsibility of the traveler to make sure they are following the laws.