So I guess it can be done from inside the UK...... You just need to be at the place of residence to sign for the mail. Here is the IPS website that states the required info and procedures (i highlight the important part)
http://www.direct.gov.uk/en/TravelAndTransport/Passports/Applyingforaneworrenewedchildpassport/DG_174107 [nofollow] First child passport - supporting documents you will need to provide
IPS needs to see original documents that prove your child is British. IPS does not accept photocopies of documents or documents that have been laminated, but will accept documents that are laminated for Braille labelling.
A birth certificate is not considered absolute proof of identity. Even if your child was born in the UK, IPS may ask to see further documents.
The documents IPS needs to see depend on where your child was born.
If you are still not sure what you need to send after reading the details below, you can call the IPS Passport Adviceline 0300 222 0000.
If the child was born or adopted in the UK
IPS needs to see the child's full birth or adoption certificate showing parents' details and one of the following:
* the mother's UK birth certificate, or her Home Office certificate of registration or naturalisation, or her passport that was valid at the time of the child's birth
* the father's UK birth certificate, or his Home Office certificate of registration or naturalisation, or his passport that was valid at the time of the child's birth* and the parents' marriage certificate
Note*: if the passport expired before the child's birth, you need to send the passport on which the father entered the UK.
If the child was born outside the UK
IPS needs to see the child's full birth or adoption certificate showing parents' details and one of the following:
* the mother's UK birth certificate,* or her Home Office certificate of registration or naturalisation, or her passport that was valid at the time of the child' birth
* the father' UK birth certificate,* or his Home Office certificate of registration or naturalisation, or his passport that was valid at the time of the child's birth and the parents' marriage certificate*
Note*: if the child has a birth certificate issued by a British consulate or high commission, you can send that instead of birth/marriage certificates.
If you are sending the father's documents, IPS also needs to see the parents' marriage certificate if the child was born before 1 July 2006.
If the child was born outside the UK but has a certificate of naturalisation or registration from the Home Office
IPS needs to see:
* the naturalisation or registration certificate
* the passport on which the child entered the UK