Although personally, I don't have a problem with using another branded engine oil in my car as long as it's of equivalent quality but the reason I take my car to Honda to have a service is for the peace of mind through knowing that the Honda mechanics will do things by the book, using parts and consumables as recommended by Honda. This is something I'm happy to pay a little extra for.
However, I have an old FRV which I just take to a local independent garage who uses Shell oil and other OEM quality parts for servicing which has been just as good except they don't change nearly as much as Honda.
If Honda are charging that extra premium for an oil service, they ought to give you Honda branded oil, it's what you paid for, whether or not Morris oils are as good as Honda is irrelevant. What's stopping them putting ASDA's own branded oil in your car and telling you that it's just as good as Honda's oil?
I would be curious to find out what it says on the receipt, does it say Honda oil? If they charged you the price for Honda's oil (can check with their parts dept) and then put Morris oil in, I would take it up with them.