I think that most of what you need to know has already been said, though I would iterate in your case that it would most likely be a waste of time going directly to a specific bank. The reason being, yes, a bank will not charge you a broker fee, but they can only offer their own products on their own criteria. Your circumstances are a little more complex than some other people, so you could absolutely benefit from an experienced broker. If you spend an hour or more sat down with a bank adviser and later find out they can't help you, that would have been a waste of your time.
The main sticking point is going to be your lack of duration in the UK and your citizenship/visa status. If you are not a UK/EU citizen, some lenders will not lend to you at all unless you have a permanent right to reside. Many will lend to you without the permanent right to reside, though this is different from lender to lender, but mostly focuses around the length of time you have spent in the country and the remaining time left on your visa.
There is a squeeze on 10% deposit mortgages at the moment, they are certainly available, but not in great quantity, and the ones that are, at considerably greater cost than if you were to have 15% deposit. One hopes this is a temporary situation! Though once again, a broker can help you negotiate around this.