Promoting New Company While Working For Old Company

My colleague and I want to start our own company, doing similar web development service that we do in our current company. Current company has a department (us) that does web development, but is not an agency or web development service. We want to create a web development agency. We are currently employed there still.

Can we show potential future clients the publicly available pages that we’ve created, whilst still being employed by our company? What about data regarding conversion rates and improvements we have made? This data isn’t sensitive, and is only relevant insofar as it shows how much improvement we can made for others, and what we can offer to future clients. And could we do this in future, when not employed by the company?

We are located in the EU.

Thank you for your advice

Edit: changed the language from web design to web development for accuracy