An MCB (miniature circuit breaker) would not have been able to
take the current load and would have tripped off at the first
switch on of the shower.

Unlikely. A Type B MCB would have required a minimum of between 90A and 150A
to trip as soon as it turns on (I can't remember the Type 2 characteristic).
To trip on 37.5A, it would require many minutes to trip, if it bothers at
all.

Christian.