Marketing is one of the professions where being better qualified will improve your chances of finding a job but you will still be able to enter the profession if not.
For those without a degree, it would be worth investing in doing the Certificate in Marketing from CIM. For those with one, any subject is fine and preferably you should have a 2.2 or 2.1.
If you have chosen a marketing or business course as an undergrad, your chances will be further improved. This will improve again if you have a postgrad in a related area or completed any professional qualifications.
What is importance is highlighting the skills you have which are important for becoming a marketeer. These may come from your academic background but also any work experience you may have gained (paid/ unpaid/ extracurricular activities). For further information on what these are read our marketing skills article.