Whatever documents you submit to UKVI (or any other visa-issuing agency) should state only true facts. If the application asks when you began work in Cyprus, tell the truth. If the application asks when you became a customer of the bank, tell the truth. One should tell the truth because none of us know what information UKVI has, nor what kind of investigation they might make.
Perhaps in completing the application some things (e.g., why you were working in Cyprus before your work permit was issued) must or should or can be explained. For instance, there may have been a good human reason (not a legal reason) to begin work before officially being permitted to do so. Your explanation gives you an opportunity to demonstrate your honesty.
Remember that UKVI will be focused on deciding if your application shows that you will indeed leave the UK on time. This may be demonstrated by the applicant showing ties and relationships to the applicant's home country. Review this SE:Travel page for a beginning discussion of this issue. In other words, UKVI will look to see if the applicant will be motivated to leave on time, rather than motivated to go underground in the UK and live and work there.
If UKVI find you've misstated facts or lied, your application will be denied and you may earn a ban. UKVI could make such a finding through seeing inconsistent statements in your application, or inconsistencies between the documents you submit and your statements, or inconsistencies between anything in your application and any information UKVI has collected elsewhere.