Certainly NOT 'solely' GB that doesn't feel it.
Figures from:
http://ec.europa.eu/public_opinion/topics/fs5_citizen_40_en.pdf
"The feeling of being European varies significantly
between Member States: 77% of citizens feel
European in some way in Luxembourg, and at least
two-thirds feel the same in Croatia (70%), Belgium
(67%) and Slovakia (66%).
This proportion falls to around a third in the UK
(33%) and Ireland (34%), and to less than half in
Greece (44%), Romania (46%), Portugal and
Bulgaria (both 48%). "
and ....
"Nearly six in ten Europeans say they “feel they are
citizens of the EU”. In Luxembourg, 85% of citizens
say this, and more than seven in ten say the same
in Malta (74%), Finland, Germany (both 73%),
Estonia (72%) and Denmark (71%). However, fewer
than half of respondents consider themselves to be
EU citizens in Greece, the UK (both 42%), Italy
(45%), Cyprus (46%) and Bulgaria (49%)."
-- So when the EU is taken as a whole, 60% feel they are European (and their own Nationality). Hardly overwhelming.
Maybe this is why they are so desperate to flood the EU with non-EU nationals?