Learn from the experience. It is more than likely that all correspondence between the solicitors was marked "Subject to Contract/Contract denied" and that the paragraph set out below was in all letters.
"Please note that we do not have any authority either express or implied to bind our clients in any way and we must emphasise that neither this correspondence nor any negotiations had between our clients shall constitute a note or memorandum within the meaning of the Statute of Frauds until such time as both contracts are signed, exchanged and a full deposit is paid."
While there may be circumstances where a Court will find a binding contract to exist even where all the formalities have not been observed it is generally the case that until such time as both contracts are signed, exchanged and a full deposit is paid that there is no binding contract.
So, no you have probably do not have any recourse.
mf