Part NCO covers Non-Commercial flight in Non-Complex Aircraft and requires the following documents to be carried:

The  following  documents,  manuals  and  information  shall  be  carried  on  each  flight  as  originals or copies unless otherwise specified:

1) the AFM (Aircraft Flight Manual / Pilot Operating Manual), or equivalent document(s);
2) the original certificate of registration;
3) the original certificate of airworthiness (CofA);
4) the noise certificate, if applicable; 
5) the list of specific approvals, if applicable;
6) the aircraft radio licence, if applicable;
7) the third party liability insurance certificate(s);
8) the journey log, or equivalent, for the aircraft;
9) details of the filed ATS flight plan, if applicable;
10) current and suitable aeronautical charts for the route of the proposed flight and all routes along which it is reasonable to expect that the flight may be diverted;
11) procedures and visual signals information for use by intercepting and intercepted aircraft;
12) the MEL (Minimum Equipment List) or CDL (Configuration Deviation List), if applicable; and
13) any other documentation that may be pertinent to the flight or is required by the States concerned with the flight.

Items listed in BOLD must be carried on each flight. ALL items must be carried if flying outside UK Airspace, i.e. London and Scottish FIR's.

The remaining documents may be left at the aerodrome or operating site when the aircraft is operating solely within the London and Scottish Flight Information Regions (FIR).

Further guidane:

See CAA website.
CAP 1415 Quick guide
EASA Acceptable Means of Compliance

The following documents are to be carried:

1) the AFM, or equivalent document(s);
2) the original certificate of registration;
3) the original certificate of airworthiness (CofA);
4) the noise certificate, if applicable; 
5) a copy of the declaration as specified in ORO.DEC.100 and, if applicable, a copy of the authorisation as specified in ORO.SPO.110;
6) the list of specific approvals, if applicable;
7) the aircraft radio licence, if applicable;
8) the third party liability insurance certificate(s);
9) the journey log, or equivalent, for the aircraft;
10) the aircraft technical log, in accordance with Annex I  (Part-M) to Regulation (EC) No 2042/2003, if applicable; 
11) details of the filed ATS flight plan, if applicable;
12) current and suitable aeronautical charts for the route/area of the proposed flight and all routes along which it is reasonable to expect that the flight may be diverted;
13) procedures and visual signals information for use by intercepting and intercepted aircraft;
14) information concerning search and rescue services for the area of the intended flight;
15) the current parts of the operations manual and/or SOP or AFM that are relevant to the duties of crew members and task specialists, which shall be easily accessible to them;
16) the MEL or CDL, if applicable;
17) appropriate notices to airmen (NOTAMs) and aeronautical information service (AIS) briefing documentation;
18) appropriate meteorological information, if applicable;
19) cargo manifests, if applicable; and
20) any other documentation that may be pertinent to the flight or is required by the States concerned with the flight.

Items listed in BOLD must be carried on each flight. ALL items must be carried if flying outside UK Airspace, i.e. London and Scottish FIR's.

The remaining documents may be left at the aerodrome or operating site when the aircraft is operating solely within the London and Scottish Flight Information Regions (FIR).

Further guidance:

See CAA website
EASA Acceptable Means of Compliance