This is the wrong forum to be asking this question. You will need to ask this in the UK/Europe law forums.
Here are a few questions for you. Answer them honestly:
1. Under what visa did you first go to the UK?
2. Did you apply for asylum when you had a valid visa or were you caught with an expired visa?
2. What were the grounds that you applied for asylum?
3. What were the statements given when UK dismissed your asylum?
Remember one thing...UK is networked into EU along with a few western countries like US...so even if you were to apply for another visa for another country..chances are good that they will find out that you have been rejected for asylum