When your offer is accepted, the estate agent should take the property off the market. This makes it less likely for other buyers to make a counter-offer. Bear in mind that offers are not legally binding until you and the homeowner have exchanged contracts.
Before exchanging contracts, make sure you have all the information you need on the property, such as what's included in the offer, and that you have a mortgage offer in writing. Once contracts are complete, the solicitors will go through them together make sure everything is correct. Once contracts are exchanged, you will be legally obliged to go ahead with the purchase. This process can take between 8 and 10 weeks.