By law, you are allowed to run a start-up of your own while under the employ of another company. That being said, depending on your contract, if your company presents a conflict of interest with your day job, you could end up in trouble with your employer.
You should also be careful that you don’t breach any intellectual property laws with your new business. Make sure that whatever service or product you provide is clearly separate from your day job. For example, if you design a product using your employer’s equipment or materials, or even if the design is made on company property, you could end up in legal trouble.