The only restriction on the type of bill which can be introduced in the senate is that they are not allowed to introduce a "money bill". Any other bill can be introduced in either house. See articles 20 and 21 of the constitution.
The UK cabinet currently has two ministers, Baroness Amos and Lord Falconer of Thoroton who are members of the house of Lords.
"The pathology is to want control, not that you ever get it, because of course you never do." -- Gregory Bateson