You asked what the law is. If they are council owned allotments, then there is a good argument that the Allotments Acts apply.
Section 1 of the 1922 Act lists the grounds on which a (council) allotment tenancy may be ended ('determined'):
(a) a six months’ or longer notice to quit expiring on or before the sixth day of April or on or after the twenty-ninth day of September in any year; (i.e. no-fault ending of the tenancy)
(b) [really can't see this applying]; or
(c) [really can't see this applying]; or
(d) [really can't see this applying]; or
(e) re-entry for non-payment of rent or breach of any term or condition of the tenancy.
However,
section 1 of the 1950 Act extends the period in (a) to 12 months from 6 months.
Section 2 of the 1922 Act sets out compensation that a tenant is entitled to, but it only applies to (b) - (d) above. So if they are giving you notice to quit on (a) or (e), you're not entitled to compensation unless the tenancy contract provides for it.
The only other part of section 2 is that If the tenancy is terminated on the on the 29th September or the 11th October, or at any date between those days, then the tenant shall be entitled at any time within twenty-one days after the termination of the tenancy to remove any crops growing on the land.
Contracts are not my thing, but given the existence of the Allotments Acts, I think your reference to offering a remedy for breach of contract is a non-starter. They have to comply with the Acts but should at the very least offer you the chance to remove personal items.
I would complain to your local councillor rather than just go along with the council's advice to sit tight and do nothing. And get in touch with the national association of allotment gardeners, who are experienced in such matters.