Short answer: Your mother appears to be a British citizen (by descent) as well as Irish, since her own father was born in Northern Ireland and her parents were married. Submit your grandparents birth certificates + marriage certificate, as well as your mother's birth certificate, etc., as part of the support for your passport application. Keep copies for reference.
Longer answer: (if your mother was not a British citizen, and solely an Irish citizen). Law and policy is not well described in the standard guidance documents. But the detail is in two policy documents- Home Office EEA free movement rights and the Passport Office policy document on Immigration & Right of Abode (but- not in the Passport Office policy on Treaty Rights itself).
From the Home Office policy:
https://www.gov.uk/government/uploads/s ... idance.pdf
(extracted from pages 19 and 20).
"Citizens of the Irish Republic, whether exercising EEA free movement rights or not, are not normally subject to any form of immigration control on arrival in the UK because of the republic’s inclusion in the Common Travel Area (section 1(3), of the Immigration Act 1971). ..."
"The 2000 and 2006 regulations do not affect the position of EEA nationals entitled to remain indefinitely on some other basis, for example because they:
- have been granted indefinite leave to remain under the Immigration Rules
- are entitled by virtue of diplomatic status to exemption from UK immigration control
- benefit under the Common Travel Area provisions as Irish nationals
Persons in this category should continue to be regarded as free from any restriction under the immigration laws on the period for which they may remain."
Passport Office policy on Immigration & Right of Abode:
https://www.gov.uk/government/uploads/s ... -abode.pdf
(page 6)
Irish citizens
Irish citizens are not subject to restrictions when they travel to the United Kingdom. In order for their child to gain British nationality, they would have to be considered as resident here in order to fulfil the requirements of the Act.
Irish citizens may be automatically accepted as settled for the purpose of section (1)(1)(b) unless there is clear evidence to the contrary. For example,if staff were advised that the parent was on a short visit to the UK, or that long periods of residence had been spent outside the UK, it would be appropriate to ask the applicant for further clarification.
The Passport Office should issue a British passport on application, but it can't be guaranteed that every caseworker knows about this policy. Especially as it's not in the Treaty Rights chapter of their instructions. If you have problems with the Passport Office (unlikely if you can show your mother is British), a Home Office nationality status letter will be accepted as stand-alone evidence of British citizenship.
https://www.gov.uk/government/publicati ... us-form-ns
Irish Citizenship: Also- your Irish citizenship is
by descent and as a result, if you want any U.K. born children to be Irish they need to be registered as Irish citizens (Foreign Birth Registration). Unless they are born in Northern Ireland, or get Irish citizenship automatically from the other parent.
This is not intended to be legal or professional advice in any jurisdiction.