is it possible to transfer revenue from my current self employed status to a new formed ltd. company?
Yes of course it is possible. You can do this either as personal investment into the company (could be offset against your directors loan account which is payable back to you from the Ltd company) or you could make the app a ltd company's asset, associate a value to it and that money is now owed to you too, as if the LTD company bought an external app. This loan or deficit is removable from turnover before tax is due. But that all depends how you set up your company and how you pay wages or distribute dividends. You need a professional accountant to advise taking into account all the factors at hand. Most importantly, this seems like a good vehicle to start a company with, so if you plan to grow, probably the way to go. But that depends on your plans of course.
If we make an assumption that revenue will be between £5k and £10k a month, is this a more tax efficient way to collect my revenue?
As Wesley Long pointed out in a comment above, this is what accountants and tax professionals are for. This is simply impossible to answer in any meaningful way without a full picture of your aims, plans and current financial position. (ie More efficient than what?) You are well advised to spend a few hundred of your monthly income to pay for some professional advice.