All training records and checks (OPC, LPC, line check, route competence, duty times..) must on request be presented to the respective authority by training department of your company. Aside of recording your flight time (in any form conforming to 1.080 - paper, electronic, even with chalk on your bathroom wall), you personally don't need to possess any of these documents.
Interesting that you have been asked to show your log book.. I had two SAFA inspection in France and one in Serbia in the last 6 months and they didn't care to ask about it.
CAA can request to have your logs inspected anytime, but not 'on-the-spot'. What is undue delay anyway.. one day.. until next divorce?
(d)
Presentation of flight time record
(1) The holder of a licence or a
student pilot shall without undue delay
present his flight time record for inspection
upon request by an authorised representative
of the Authority.
(2) A student pilot shall carry his flight
time record logbook with him on all solo
cross-country flights as evidence of the
required instructor authorisations
It's too valuable (and heavy 
) to be carried around 