From what i remember when i bought my first place last year, you dont need a mortgage to put in the offer, but they will want proof pretty sharpish, so you should get an offer 'in principal' (as stated above) so you know you can afford the property you are putting the offer on.
It can take a few days to get the offer in principal, so you should see a Mortgage Broker first to get an idea of what you can borrow.
On a separate matter, any decent Mortgage Broker will not charge you a fee, they take their cut from the mortgage provider (just something to be aware of).