Can you have 4 card straight in poker?

I was playing Texas Holdem at lunch today, when I lost on a round and my mate said that I actually one that round. He said in the British version, of the game, (were English by the way) you can have a small staright or a similar name , and have 4 consecutive cards rather then 5. I didn't believe this and said it's Texas holdem not British holdem, there are not britsh rules. Does this mini straight exist and If so, what beats it and what does it beat