I have received a conditional offer from the University of Birmingham and an unconditional offer from the University of Leeds for a masters degree in marketing, both programs are great but I have a deadline to accept Birmingham's offer so I was wondering if I could accept both offers and then decline one of them.
If the programs you are interested in have a limitation regarding how many new students they take in each term, you should probably not accept both offers. It could mean that someone else interested in a slot would potentially not be accepted into a program. There might be the possibility of extending the deadline, and it won't hurt to ask them. I understand it's hard to decide on a program, but you should save others' time and effort by first deciding, then accepting. There is no hard requirement that I know of, however, that explicitely prohibits you from doing otherwise.
Make sure to make an informed decision, e.g. check the curriculum for both programs.
Call AND email Birmingham and tell them that you have a firm offer from Leeds and conditional from Birmingham.
See if you can convert Birmingham to a firm offer or at least to extending the deadline. Hey...you're a marketing person. Negotiate. ;-) [Remember the scene in breaking bad where Walt tells Jesse "you're a drug dealer, negotiate".] Seriously, give it a shot and see how you do. Nothing changes when you are looking at job offers.
If they hold firm, I would just not respond (rather than decline) the Birmingham offer. I have learned in both academia and business that sometimes these deadlines get waived when they want the candidate and he doesn't answer. But you should be ready to let the conditional (i.e. not very good) offer from Birmingham expire if they are firm.