Tax codes with the HMRC can be a bit hit and miss. If they do it correctly, your tax code with your employer will remain the same, and the tax code they issue to your new ltd company will be 'BR'.So ideally, your currently employer will not know.

One option you could consider is not registering your company for PAYE (and if you already have, then just don't put yourself on the payroll). As you already have a full-time job and (I assume) earn more than £7,475 per year, then the tax advantages of paying a salary through your new ltd company will be very small anyway.