My brother and I have been left a house by my late mother, I only work part time and I would like to know if I could borrow money secured on my half of the property to buy my brother out?
Generally, no. A mortgage is a lien against the property, which allows the bank to exercise certain options, primarily Power of Sale (Force you to sell the property) and outright seizure. In order to do this, title needs to be clear, which it isn't if you have half title.
However, if you have a sales agreement, you can buy your brother's half, and then mortgage the entire property. This happens all the time. When you buy a house from someone, you get pre-approved for that house, which, at the time, you have no title to.
Through some black magic lawyering and handwaving, this is all sorted out at closing time.