As soon as you have accepted a job offer, this forms a basic legal contract between you and your new employer, even if you haven't yet received anything in writing. Often job offers are expressed to be subject to receipt of 'satisfactory' references. However, if the prospective employer doesn't mention this at the time, it can't add this condition later on.
If an offer that has been accepted is then withdrawn, your employer has 'breached' the contract. It may be possible for you to sue your new employer as a result, if you have suffered loss, for example because you have left your previous job to take up the new offer.
If a court decides that your contract was breached, it can order your employer to pay you damages or compensation. However, this is usually limited to the wages you would have earned during the contractual notice period under the new contract.
If your employer withdraws the offer for an unlawful or discriminatory reason, for example because the employer finds out that you have a disability, this will be disability discrimination. No service is needed for this kind of claim.