As a general principle, yes they can. Where a public body promises to do something and a person has reasonably relied on that promise then they should be entitled to rely on the public body to do what it says it will do. This principle is know as legitimate expectation. Where it is established that the public body has made a decision without complying with any promises it has made, then it risks having those decisions overturned by the Courts.
In the recent case of R (on the application of Save Britain's Heritage) v Secretary of State for CLG  EWCA Civ 2137 the Court of Appeal reaffirmed this principle as per the quotation below. The case itself involved the proposals for a 24-storey glass tower, designed by Renzo Piano, immediately adjacent to Paddington Station. The claim stemmed from a Green Paper issued by the Government in 2001 which said that from then on reasons would be given for not calling in planning applications. Call-in is the process whereby a local planning authority has to refer certain types of significant planning application to the Secretary if State who then decides whether to deal with the application themselves or refer it back to the local planning authority to determine.
In this case, having promised to give reasons for not calling in planning applications, and having not withdrawn that promise (although it was argued otherwise), the Secretary of State was bound to give reasons for not calling-in this planning application and there was a legitimate expectation that they would do so.
Accordingly, there is the highest possible authority for the proposition that, if a public body indicates a clear and unequivocal policy that will be followed and applied in a particular type of case, then an individual is entitled to expect that policy to be operated, unless and until a reasonable decision is taken that the policy be modified or withdrawn, or implementation interferes with that body’s other statutory duties.