The term "Mean High Water Interval" (MHWI) is now usually used to replace that of 'Luni-Tidal Interval'.
For your information, this term refers to the interval between the Moon's transit (upper or lower) over the local or Greenwich Meridian and the time of the following High Water, i.e. it is the time lag between the passage of the Moon and the arrival of the next High Water at a particular location.
Thus the Mean High Water Interval refers to the average of all such High Water intervals, for all transits of the Moon, over a particular period of time.
You may wish to consult Admiralty Co-Tidal Chart 5058, "Co-Tidal & Co-Range Lines: British Isles and Adjacent Waters". This chart displays Co-Tidal lines drawn through points of equal Mean High Water Interval, and Co-Range lines drawn through points of equal Mean Spring Range. Full instructions on how to use the chart are published on it. However, this chart is specifically aimed at obtaining tidal predictions at offshore locations, but could possibly be used to obtain either:-
This chart, as with all of our publications, is available from any Admiralty Distributor listed at www.ukho.gov.uk/how_to_buy.html.
Therefore at Dún Laoghaire, Ireland, MHWI = 1128 GMT.
Interval is 32 minutes (1200-1128)"