Yes. A blanket ban on using the employer’s computer system to send personal emails is not against the law. However, good employers will allow their staff some personal use of the email and web, provided this is used responsibly and doesn't interfere with work or the employer's reputation. Check your employer's email usage policy, which will define your rights in this area.
The best way to conduct any personal email communications at work is to use a private email address rather than your work one, as long as your employer's web usage policy allows this. Web-based email services such as Gmail, Hotmail and Yahoo! Mail can be accessed via a web browser from any internet connection. However, no email system is completely impregnable, although an employer that intercepted and read your private emails sent through a non-work web-based email service using the company’s computer system is very likely to infringe your privacy rights except in very exceptional circumstances.
Clearly, if there is a blanket ban on making personal use of the employer’s computer system where you work, then if you are caught sending personal emails at work this could have disciplinary consequences, whether you use the employer’s own email system or a service provided by a web browser.