Hello and thanks for using Just Answer.
I am Al and am happy to assist you with your enquiry.
It is good practice and indeed morally right for a Seller not to accept any other offers, once a Sale has been agreed. However, until Contracts have been exchanged, either party is entitled to withdraw from a Sale without any penalty.
Likewise, even once a Sale has been agreed, a Sellers Estate Agent is under a duty to notify the Seller of any further offers they receive, at any time upp to the date Contracts are exchanged. 9 times out of 10, the Seller would not accept any subsequent offer, but I'm afraid it comes down to the individual and his morals.
As you are first time Buyers with a large Deposit, I would certainly hope that the Seller will stick with you, as you are going to be in as good a position as anyone else, apart from a cash Buyer who has no Sale. However, you may indeed have to increase your offer if it turns out the Seller is after the best possible price. You then have to decide whether you are prepared to make an increased offer, or whether you just walk away.
I hope this assists and sets out the legal position.