Postgrad applications tend to ask only for university grades, but if you've got good A Levels, there's no harm in popping in a supplemental sheet stating what they are, along with your transcript, references and personal statement. I did this and got offers from everywhere I applied.
If you got a 1st, you would be in a good position to apply to Oxbridge, even thought you're right in saying that there will be an element of university tier bias when it comes to what your 1st is worth.