British thinking on Europe has always been a contradiction.
Euro scepticism is built on the simple emotion that British people don’t like foreigners making their laws for them.
On the other hand there are obvious advantages to being a powerful influence in a powerful EU, as opposed to begging for first satellite status to the US, and getting nothing in return.
Many areas are policy (competition law, consumer protection, the environment, and even immigration and foreign policy) are more effectively dealt with at a pan-European level.
Britain will not be leaving the EU, so it is important that British politicians are effective in fighting for their interests and their designs for Europe, not shuffling off to the sidelines.