The one thing the office does
The Legalisation Office has a single job. It keeps a record of the signatures and seals used by British public officers, and when your sheet arrives it checks the mark on that sheet against its own record. If the two agree, it prints a certificate and fixes it to the paper. That act is complete, honest and narrow, and it is finished by post from a PO box in Milton Keynes.
Why that is not the end of this route
The certificate works because a group of states agreed to take it from one another without further checks. The Democratic Republic of the Congo sits outside that agreement, so its offices are not set up to read the certificate, and consular attestation carries the paper instead. There is no such product as an apostille issued in Birmingham for use in Democratic Republic of the Congo, however well the phrase reads.
Four things it cannot do for you
It cannot make a foreign office accept anything, because acceptance is not a British act. It cannot read your paper and tell you whether the content answers the question you were asked. It cannot see you in person, since it runs on post alone and has no public counter anywhere. And it cannot speed up a stage that belongs to another state's mission.
None of that is a failing. An office that certified more than it knows would be worse, not better, because the value of the certificate comes from how tightly it is defined. Knowing where a stamp stops is what stops you paying twice, and it is the difference between a file that moves and a file that circles.
Where that leaves your paper in Birmingham
Your work in the city is the part you fully control. Choose the sheet, order a fresh certified copy of any civil record from Birmingham Register Office at Holliday Street, and count how many finished papers the far end will keep. Sending an apostille from United Kingdom to Democratic Republic of the Congo is not the plan; building a clean file for the consular route is.
Time the job around the stage you do not run. The British side is predictable and priced per sheet, so it is easy to slot in. The consular side sets its own pace, and a file that reaches it complete on the first attempt is the only real way to keep the whole thing short.