It's hard to say and would depend on the rights in question. Parliamentary sovereignty would mandate consulting parliament, but our parliament is representative, not direct. It would also be necessary to consult devolved kingdoms, but the extent to which required is not clear.

We don't really have the same segregation of powers. Primary legislation can come from various sources and apply in various ways to various parts of the UK. The judiciary is independent and is generally relied on to determine how those laws are to be interpreted.

In order for laws to come into force nationally, they need royal assent from the Queen. If memory serves correct this relies on the Queen literally saying the word "Approved" at a certain point in the reading of a law. It might've changed, but might still be in effect. As such we don't really have the same concept of Executive Orders. We do have written guidance on laws, but this can be overridden through the courts.