Government and Identity
The nearest passport agency office is in London.
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They need any current passports, a birth certificate, two proofs of identity/address, the application form, certified and un-certified picture and the fee.
A birth certificate can be applied for online from the General Register Office if you know all the details, include year of registration. If you don’t know them then you need to get a GRO index number, this is very tricky since you need to visit a physical copy of the index and it seems the GRO don’t keep it any more. It might be at Kew and the City of Westminster archive may have a copy.