The reality is that the national payment systems, including cheque clearing systems, have not so far been harmonised and there are no short term plans to develop a standard cross border system. In any event there would seem to be particular difficulty associated with developing a cross border paper based system.
Yes, inflation was falling quite strongly prior to the 1989 Act becoming law on 1 February 1990, but of course the Bank had been acting under instructions from the Minister to focus exclusively on reducing inflation since at least 1985, and to  BIS Review 78/1999  4  focus on achieving a 0 to 2 per cent target since April 1988.