Is A Conditional Job Offer A Binding Contract?

It depends. 

In Kankanalapalli v Loesche Energy Systems the Claimant was offered a job as a project manager subject to receipt of satisfactory references and a right to work check. Mr K accepted the offer and began taking steps towards starting his new job. When the company withdrew the offer before his start date for reasons which were unrelated to references or the right to work check, Mr K argued that this amounted to a breach of contract due to lack of notice. 

A first instance employment tribunal found that no binding contract had arisen because the conditions of the offer (references & the right to work check) had not been satisfied and therefore the employer was entitled to withdraw the offer and no right to notice arose.