Privity in Contract Law, is a doctrine which prevents third parties from interfering with those "privy" to a contract.
The issues usually relevant whenever there is doubt brought to the doctrine is when it is argued that a third party has an actionable right in such.

The general law is that parties not privy to a contract cannot rely on the benefits conferred within, which would include negative ones such as exemption or limitation clauses.
This was outlined in Midland Silicones v Scruttons. There are exceptions in existence however.

One of them is a successfully "drafted Himalaya Clause". It would be effective, as was the case in The Eurymedon in transferring such third party benefits.
In the past, such a clause would require a skilled draftsman to carefully plot. These days however, it is easier for contracts to confer vicarious immunity.

Usually the statute to look for would be for contract rights of third parties act. America, in the form of Cardozo has gone about it slightly differently.

If CRTPA is applicable to your country, usually section 2 would cover everything.

Cl 2(6) covers exclusion clauses, 2(3) limits it to parties expressly provided for, and 2(1) covers the actual purporting of benefit.

Contracts branched in such a way are still subject to the usual clause control as covered in Contract Creation and Management.

If the crtpa isn't comprehensive enough for your peculiar or particular purpose, then you might have to look at another matter.

This would be the albazero exception.

In this case, often the primary question is whether a 3rd party can claim substantial damages for losses suffered.
In some cases however the parties privity to a contract must claim for the third.

There are two exceptions, which we will refer to as "the narrow ground" and "the broad ground" respectively, to the general rule that the plaintiff/promisee can only recover nominal damages for a breach of contract where it has suffered no loss (for instance, where the substantial loss is suffered by the third party who is the intended beneficiary of the contract).

Of that, we are only concerned currently with the narrow ground, and the broad ground could be considered later.

The narrow ground permits the plaintiff/promisee to recover substantial damages on behalf of the third party. In contrast, the broad ground permits the plaintiff/promisee to recover substantial damages for its own benefit on the basis that it is recovering for its own loss.

Narrow ground exceptions to the general rule was that a plaintiff can only recover damages for his own loss.
The contract was for a large development of property which, to the knowledge of both Corporation [the plaintiff/promisee] and McAlpine [the defendant/promisor], wasgoing to be occupied, and possibly purchased, by third parties and not by Corporation itself. Therefore it could be foreseen that damage caused by a breach would cause loss to a later owner and not merely to the original contracting party, Corporation.

The Albazero was to cover the case so as to hold that where A enters into a contract with B relating to property and it is envisaged by the parties that ownership of that property may be transferred to a third party, C, so that the consequences of any breach of contract will be suffered by C, A has a cause of action to recover from B the loss suffered by C. However, two points are clearly established by the decision in both The Albazero and the St Martins case [ie, Linden Gardens]. First, A is accountable to C for any damages recovered by A from B as compensation for C's loss: The Albazero, at p 888D. Second, the exceptional principle does not apply (because it is not needed) where C has a direct remedy against B: see the The Albazero, at p 848, and the decision itself which, whilst recognising the exception, held that it did not apply to that case since the consignee of the goods had a direct claim

In essence, the exception to Albazero exception was a black hole with no direct remedy.
As the DCD was an integral part of the contractual arrangement, there was really no room for the application of the [rule in] Dunlop v Lambert or The Albazero exception.

The rule provides "a remedy where no other would be available to a person sustaining loss which under a rational legal system ought to be compensated by the person who has caused it."
In the narrow ground, it is important to note the condition that the plaintiff/promisee, where it recovers substantial damages which represent the third party's loss, must account to the third party for such damages

In the scenarios you might face, it might be such there was no such deed emanating from either parties.

The fact that under general law, that subsequent purchasers may have a limited right to claim in tort against Civic and the appellants, cannot justify the taking away of the contractual rights of the building employer under The Albazero exception. Such a limited right does not remove the legal black hole completely. A claim in tort is not a "provision of a direct entitlement" and it is subject to establishing proximity and foreseeability and defences such as independent contractors. Thus, that sometimes a case falls within the narrow ground of the exception expounded by Lord Browne‑Wilkinson in St Martins and affirmed by the majority of the House of Lords in Panatown. To deprive a building employer of The Albazero exception, there has to be an express contractual right in favour of [the] third party or something akin to it

An extremely important point is that the two exceptions are conceptually inconsistent with each other. Hence,

they cannot apply simultaneously. The crucial issue that arises, as a result, is whether – and, if so, how – the two exceptions can beapplied in a consistent and coherent manner. To this end, there ought to be an objective legal point which, when reached, will result in the broad ground being applied in place of the narrow ground.