The presence of ordered oxygen vacancies in perovskites governs magnetic phase stability owing to changes in crystal-field splitting with different anion geometries, polyhedral arrangements, and electronic configurations of the transition-metal cations. Here we use density functional theory calculations to assess the magnetic phase stability of

{Sr}_{2} {Fe}_{2} O_{5}

(with a

d^{5}

electronic configuration) and

{Sr}_{2} {Mn}_{2} O_{5}

(

d^{4}

configuration), exhibiting the

{Ca}_{2} {Mn}_{2} O_{5}

-type oxygen-deficient perovskite structure, with hydrostatic pressure. The

{Ca}_{2} {Mn}_{2} O_{5}

-type structure is composed of square pyramidal units, the crystal-field splitting and polyhedral connectivities of which support different ground-state magnetic orders depending on

d

-orbital filling: E-type antiferromagnetic (AFM-E) for

{Sr}_{2} {Mn}_{2} O_{5}

(

d^{4}

) and G-type antiferromagnetic (AFM-G) for

{Sr}_{2} {Fe}_{2} O_{5}

(

d^{5}

). We show that hydrostatic pressure enhances the crystal-field splitting and affects the magnetic stability. We find that the AFM-E order exhibited by

{Sr}_{2} {Mn}_{2} O_{5}

is robust over the surveyed ranges of applied pressures, whereas

{Sr}_{2} {Fe}_{2} O_{5}

shows a magnetic transition from AFM-G to ferromagnetic spin order at

\approx 24.5

GPa. We also discuss the effect of correlation strength, treated using the Hubbard

U

correction, which we find suppresses a spin crossover transition in

{Sr}_{2} {Fe}_{2} O_{5}

and shifts it to higher pressures.

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