There is no law currently to say that you are entitled to bank holidays as holiday. The government did announce in its manifesto at the recent General Election that it plans to change this.
The circumstances are dependent on your individual Contract of Employment with your employer.
They are within their right to stipulate that any holiday you are given, in your case 23 days, can include the 8 statutory bank holidays! (This does not mean this is fair though)
The law does state that you are entitled to a minimum of 4 weeks paid leave, you are getting 3 days extra.