The following is from the UKPA website:
For my own passport application my next door neighbour of ten years countersigned my application, he was a retired police officer.Section 10 - Countersignature
If the application requires countersigning, the application form must be completed before it is countersigned. A countersignature is usually only needed if the application is for a first passport or to replace a lost, stolen or missing passport. A countersignature may be needed if the renewal or extension of a passport and the appearance of the holder has changed considerably, for example if the passport was issued when they were a small child.
The countersignatory must hold a current British or Irish passport, and be willing to provide their passport number in the relevant space in section 10.
ACCEPTABLE COUNTERSIGNATURES
Accountant
Articled Clerk of a Limited Company
Assurance Agent of Recognised Company
Bank/Building Society Official
Barrister
Broker
Chairman/Director of Limited Company
Chemist
Chiropodist
Christian Science Practitioner
Commissioner of Oaths
Councillor: Local or County
Civil Servant (permanent)
Dentist
Engineer (with professional Qualifications)
Fire Service Official
Funeral Director
Insurance agent (full time) of a recognised Company
Journalist
Justice of the Peace
Legal Secretary (members and fellows of the Institute of legal secretaries)
Local Government Officer
Manager/Personnel Officer (of Limited Company)
Member of Parliament
Merchant Navy Officer
Minister of a recognised religion
Nurse (SRN and SEN)
Officer of the armed services (Active or Retired)
Optician
Person with Honours (eg OBE MBE etc)
Photographer (Professional)
Police Officer
Post Office Official
President/Secretary of a recognised organisation
Salvation Army Officer
Social Worker
Solicitor
Surveyor
Teacher, Lecturer
Trade Union Officer
Travel Agency (Qualified)
Valuers and auctioneers (fellow and associate members of the incorporated society)
Warrant officers and Chief Petty Officers
Or persons of similar standing to the above, working or retired, are acceptable as countersignatories.
Relatives or partners should not countersign passport applications.