The Limitations Act of 1980 and its predecessors apply to civil actions brought by private individuals. It is not a criminal statute of limitations. I will answer with regard to civil cases, rather than criminal ones.
Section 40 of the Limitations Act of 1980 incorporates by reference a schedule of transition provisions that govern this question, and when a cause of action is not governed by the 1980 Act it usually defaults to the predecessor 1939 Act.
The problem is both bigger than just the fraudulent breach of trust unlimited statute of limitations under Section 21 of the Act, since the deadline only runs from when an action accrues that can be long after the act giving rise to the claim actually happened, and smaller, because the act (and also its predecessor 1939 act) allow statutes of limitations to be extended for equitable reasons under certain circumstances.
The 1881 Limitations Act, Section 27 had an exception to the general rule for concealed fraud tolling the statute so long as it was concealed, which probably carried over into the 1939 Act.
Section 9 of the transition provisions states in the relevant part that:
(1)Nothing in any provision of this Act shall—
(a)enable any action to be brought which was barred by this Act or (as
the case may be) by the Limitation Act 1939 before the relevant date;
The 1939 Act limitations ran from when the act was committed, not when it was discovered, until the 1963 Act changes that.
A full analysis of the breach of trust issue is found in this law review article.