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If you have already been advised by a legally qualified person you should go with their advice.
However it is strange that the Home Office will issue you with an adult British passport on the basis of your birth certificate when in fact it is the certificate of registration which is what entitles you to a British passport. In any event, the Home Office would have asked for any previously held passport and when you submitted your child passport, they should have queried the name. Failing all the safe guards in place, when you spotted the error why didnt you correct immediately rather than waiting 2 years.
The certificate of registration is very important. It is as important as a British birth certificate and it is what entitles you to British citizenship and not the British passport you hold.