Firstly you have to establish the type of warranty offered by BMW UK. The headlines of advertisements are almost always a little misleading. The devil is in the detail.
Most european manufacturers operating in the UK provide the vehicle with a two year unlimited mileage warranty (same as Ireland) but the UK distributor add an additional third year over the unlimited mileage for two years, but this is where it gets tricky.
The third year will only be honoured if the mileage does not exceed 60,000 miles on the third year anniversary from the date of registration or upto 60,000 miles during the third year.
Here are some examples;
18 month old BMW 320d with 75,000 miles - warranty covered until 24 months old. No third year warranty.
30 month old BMW 320d with 25,000 miles - warranty covered until 36 months old providing that the mileage does not exceed 60,000 miles at any point in the third year. If it does, warranty will not apply after 60,001 miles.
Now if you bring a vehicle to Ireland this is the situation. Upto 24 months old (for european manufactured vehicles), the Irish dealer must honour the warranty. This is enshrined in european law, however some dealers do not like to work on UK vehicles as there is more admin work involved and some don't like it because you didn't buy the vehicle from them. This is not always the case though and most are glad of the extra work (which they get paid for by the manufacturer).
The third year is a differant story though, they do not have to honour this as it is simply an add-on by the UK distributor.
Think of it in terms of getting a garage specific warranty on a second-hand car from one dealer and going to completly differant dealer asking him to honour it. He'll just tell you to go back to where you bought it.
Some dealers here will though, after they check it out with the UK who usually agree to pay them, but it is more messy (admin wise) than most dealers would like.
Hope this helps!