Sign up with GoogleIm not for 1 second implying that you don't need a degree. I definatly would not have gotten either job in the UK without a degree. I also think if a I had a medical degree I may not have been so lucky. They can be flexible here in the UK, but you always have to remember that when there is a pile of cv's in front of someone and they don't know any of the candidates, they are going to make their decisions based on the contents of those cv's.
All you have to do is make it to an interview. Once you do that its then up to you to convince them that any shortcomings in your cv are more than made up for in other areas. But if your cv isn't good enough to get you an interview its doesn't matter how nice you are, how talented you are, and whether you have the potential or not. Now there has been a lot said in these forums about how irrelevant a cv should or shouldn't be. Fact is, that its physically impossible to interview every single candidate. Especially in job markets the size that they are in UK/EU/US etc. So whether its fair or not, your cv is the key to the front door.
Good luck