I quit my job without notice. Am I entitled to be paid for the period I've worked this month?

Yes. You are entitled to be paid your wages for the hours you worked up to the date you quit your job.  

In general, it is unlawful to withhold pay (for example holiday pay) from workers who do not work their full notice unless you have signed a clear written agreement that allows the employer to make deductions from your pay. Without such a term, failing to pay your wages in full will be an unlawful deduction of wages which can be challenged in the employment tribunal.  

Be aware that your employer is entitled to refer to your failure to give proper notice in any reference they give to your new employer.