Would submarines and anti-submarine warfare advance sooner?

Could submarines comparable to the E class appear earlier in this scenario?

Possibly, but the outcome depends heavily on foreign reactions; both submarine development and anti-submarine work would likely receive more funding.

The question proposes bringing E-class-like submarine capability forward, but the scenario leaves the design unresolved. Other powers' choices would strongly affect submarine development. Both undersea weapons and anti-submarine warfare would probably receive substantial funding. The timing of a practical depth charge is another open question, so the funding premise alone does not yield a definite earlier submarine or countermeasure.