Jurisdiction: england-and-wales
Contract law
As a basic principle of contract law, you are entitled to receive what you were promised in the contract. If the contract specified that you should be able to take a large bag into the cabin without further charge, then that is what you should receive. The fact that Easyjet later changed their policy is only relevant if your contract (not later versions of the contract) specified that they could retrospectively apply such changes to your booking (but in that case see below for applicable consumer law in relation to unfair terms).
By failing to provide this, Easyjet have breached the contract. The standard remedy in such cases is damages. Namely, that you should be put back in the position you would have been in had the other party not breached the contract. Before the breach, you had £x in money. Hence, to put you back in your previous position, you should receive £x in money (not vouchers).
This is potentially complicated by the fact that you entered into a second contract with Easyjet at a later stage. In the first contract, you agreed to pay £y and Easyjet agreed to provide a flight and a large bag in the cabin. In the second contract, you agreed to pay £x and Easyjet agreed to provide a large bag in the hold. This distinction is important, because as a general rule past consideration (something already promised under a previous contract) isn't good consideration (you can't use it as the basis of a later contract between the same parties), but here what they have agreed for the bag is different.
There are two ways to look at this. On the one hand, your payment of £x under the second contract is a loss you incurred due to Easyjet's breach of contract under the first contract. Accordingly, Easyjet should pay you damages of £x under the first contract.
On the other hand, you could argue that you entered into the second contract under duress. At the point at which you purported to agree to this contract, you essentially had no choice but to do so. The modern definition of duress is set out in DSND Subsea Limited v Petroleum Geo Services ASA [2000] 7 WLUK 875 at paragraph 131 (emphasis added):
The ingredients of actionable duress are that there must be pressure,
(a) whose practical effect is that there is compulsion on, or a lack
of practical choice for, the victim, (b) which is illegitimate, and
(c) which is a significant cause inducing the claimant to enter into
the contract[...]. In determining whether there has been illegitimate
pressure, the court takes into account a range of factors. These
include whether there has been an actual or threatened breach of
contract; whether the person allegedly exerting the pressure has acted
in good or bad faith; whether the victim had any realistic practical
alternative but to submit to the pressure; whether the victim
protested at the time; and whether he affirmed and sought to rely on
the contract. These are all relevant factors. Illegitimate pressure
must be distinguished from the rough and tumble of the pressures of
normal commercial bargaining.
It sounds like all three elements are potentially present here. If duress is established then the contract is voidable and you could claim restitution for the £x paid under that contract.
Consumer law
Pursuant to Section 50 of the Consumer Rights Act 2015 (emphasis added):
(1) Every contract to supply a service is to be treated as including
as a term of the contract anything that is said or written to the
consumer, by or on behalf of the trader, about the trader or the
service, if—
(a) [...], or (b) it is taken into account by the consumer when making
any decision about the service after entering into the contract.
(2) Anything taken into account by the consumer as mentioned in
subsection (1) (a) or (b) is subject to — (a) anything that qualified
it and was said or written to the consumer by the trader on the same
occasion, and (b) any change to it that has been expressly agreed
between the consumer and the trader (before entering into the contract
or later).
Thus, even if the written contract does not contain a clause stating that cabin baggage was included, or contains a clause which is ambiguous or isn't in your favour, you can also rely on anything else (e.g. emails, website information) which was stated to you in relation to baggage prior to or at the time that you booked the flight. I'm less confident that this would apply to the later email as the contract was already formed by that point, albeit Section 50(1) is ambiguous about the timing of the information being given.
If Section 50 is applicable, the remedies are found in Sections 54 and 56:
54(2) - In this section and section 55 a reference to a service
conforming to a contract is a reference to (a) [...] (b) the service
conforming to a term that section 50 requires to be treated as
included in the contract and that relates to the performance of the
service.
54(3) - If the service does not conform to the contract, the
consumer's rights (and the provisions about them and when they are
available) are (a) [...]; (b) the right to a price reduction (see
section 56).
56(1) - The right to a price reduction is the right to require the
trader to reduce the price to the consumer by an appropriate amount
(including the right to receive a refund for anything already paid
above the reduced amount).
56 (4) - A refund under this section must be given without undue
delay, and in any event within 14 days beginning with the day on which
the trader agrees that the consumer is entitled to a refund.
Note that if these provisions are applicable, then Easyjet cannot force you to accept a voucher instead of cash:
56(5) - The trader must give the refund using the same means of
payment as the consumer used to pay for the service, unless the
consumer expressly agrees otherwise.
What if the original contract has a clause which allows Easyjet to retrospectively modify their baggage policy (as I hinted at earlier)? There's a very good chance that such a clause would would be deemed unfair (and therefore enforceable) under consumer law. Sections 62(1) and 62(4) of the Consumer Rights Act 2015 provide:
62(1) - An unfair term of a consumer contract is not binding on the
consumer.
62(4) - A term is unfair if, contrary to the requirement of good
faith, it causes a significant imbalance in the parties' rights and
obligations under the contract to the detriment of the consumer.
Pursuant to Section 63(1), "an indicative and non-exhaustive list of terms of consumer contracts that may be regarded as unfair" may be found in Part 1 of Schedule 2 of the Act. Depending on how your contract is worded, the following may be relevant:
11 - A term which has the object or effect of enabling the trader to
alter the terms of the contract unilaterally without a valid reason
which is specified in the contract.
12 - A term which has the object or effect of permitting the trader to
determine the characteristics of the subject matter of the contract
after the consumer has become bound by it.
13 - A term which has the object or effect of enabling the trader to
alter unilaterally without a valid reason any characteristics of the
goods, digital content or services to be provided.
14 - A term which has the object or effect of giving the trader the
discretion to decide the price payable under the contract after the
consumer has become bound by it, where no price or method of
determining the price is agreed when the consumer becomes bound.
15 - A term which has the object or effect of permitting a trader to
increase the price of goods, digital content or services without
giving the consumer the right to cancel the contract if the final
price is too high in relation to the price agreed when the contract
was concluded.
