You do not need to have your property on the market, as you may be able to fund the purchase other ways. The agent will want to inform the purchaser how you are funding to make an informed decision on your ability to proceed. You do not have to inform them of your situation but it helps.
If you make an offer the agent is under a legal obligation to report it under the Estate agents act. 79
Have you considered a bridging loan if it is the house you want?
I am a Chartered Surveyor, so do know a little about this.