Yes, you can access your account via FTP through your web browser. In order to do so, you should enter the following URL address:

ftp://YourUsername:YourPassword@YourDomain.com

Note that if you have created additional FTP account you should enter the following URL address:

ftp://YourUsername%40YourDomain.com:YourPassword@Yourdomain.com

You should use %40 instead “@” because if there is another @ you will not be able to access your account. %40 is the ASCII code for “@”
If you can’t access this way, probably your ISP has blocked port 21, which is the default port for FTP connections. If that is the case you can ask them to unblock it or you may use the FTP client in passive mode.