As far as I understand MNPS would equal RNP12.6. However MNPS regulations are not based on the RNP concept and 2 LRNS is the nav requirement. RNP 12 can be acheived with only 1 LRNS in remote areas or with none where short range ground based nav aids (VOR DME) are available.
EDITED to correct 12 to 12.6.
This from NAT 001 :-
The MNPS Concept
1.3.1 In the NAT Region, the requirement for a given standard of navigation performance has long been recognised. It was because of such a requirement that the concept of a MNPS was introduced in 1976, to allow for a reduction in track spacing from 120 to 60 NM. In effect, MNPS was the forerunner to RNP, though unlike RNP it not only specifies the position accuracy that an aircraft is required to achieve, but it also takes into account the availability and reliability of navigational information by setting out a requirement for the carriage of specific navigational equipment. (MNPS Airspace as it has been established in the NAT Region would, if RNP were to be applied, be designated RNP 12.6).