Are you getting contractual notice confused with statutory notice? The company is obliged to give you statutory notice which is determined by the length of time you have worked with the company but you have to give contractual notice ie however long was specified on your contract. What sanction would the company take if you left after 2 weeks? They could sue you for the 6 weeks work they think you owe them but that would be very expensive and unlikely to be guaranteed successfull. Anything can affect a reference, lets face it, although employment law has made it very difficult for an employer to give an unwarranted bad reference. My advice to you would be to take your contract of employment to Citizens Advice and ask their opinion. It is free after all. Good Luck, any problems come back to AB.