Do we need to mention our traveling dates different on visa application?
Of course. Always tell the truth.
Also if we fill same dates on our application, Am I possibly be asked by the immigration office why am I entering London with out him?
Of course. Anything that the immigration officer observes that is inconsistent with the visa application is a possible cause for concern, and the officer will almost certainly ask about it. That is the principal reason why you should tell the truth in the application.
In the UK immigration system, the consequences of not telling the truth are quite severe. On the other hand, traveling to the UK separately from your spouse has no negative consequences by itself. So tell the truth.
Credit:stackoverflow.com‘