Hi, thanks for your question. My name's XXXXX XXXXX I'm going to assist you with it.
Regrettably, in the absence of a lock-out agreement (pursuant to which the seller will not consider other offers during a specified period), the only remedy in situations such as this is to outbid the other party.
Under English law, all contracts transferring property must be in writing, which generally means that the agreement only becomes binding on exchange (although there are certain exceptions to this, such as public auctions).
For more information, please find below a link to guidance provided by CAB which includes a section on this issue.
I'm sorry if this was not the information you were hoping for and please do let me know if I can clarify anything.