The GRO Index does show mmn from 1837. If you want to search an extended period, say find all the children in a large family, step the date up 5 years at a time, i.e. your chosen year +/- 2years. But you have to search for males and females separately, so it's a bit tedious.
GRO will show mmns after 1924, but only if you put the name into the search, it confirms it. It only runs to 1934 anyway, because the project was not finished, and restarts at 1984. For births with no father named it shows dashes, rather than repeating the mother's surname as in FreeBMD.
There are known to be errors and missing entries, which you can report from the foot of the search page, but only AFTER you have done a search.