If you truly have nothing to hide, then why tell any lies, because sooner or later it will come back and bite you in the a***. Getting into the industry is not easy, but finding that opening takes grit and determination,something many can associate themselves with,and without lying as it were, sure be economical with the truth but be truthful.
As say for example you want to work on the line in a u.k 145, you need to submit for a Criminal Records Check, also supply the local Airport Authority with records of previous employment, which if you just simply say company has gone bust or words to that effect then they can simply request that you provide evidence from Her Majesty's Tax Office, which will indicate your employment history in the form of previous tax codes, highlighting dates and times of employment.
The main piece of advice is to keep knocking on doors, making calls, and try to get some form of works experience at a local light airfield,if there is one nearby..If there is not one nearby then just continue to explore all avenues and be honest in your approach.
I wish you luck
