What are our chances of getting a mortgage?
THE 'problem' you face is that neither of you has a permanent job - a contracted job and a relief bank job.....I think your best option is to go and see a mortgage advisor and see where you stand.
In the meantime keep saying - you need at least 10% of the asking price and you need extra ££ for surveys, legal fees etc. Also pay off any credit card debts or other loans you may have.
Look at being able to borrow about 3.5 times your income ... so are their properties you can afford in that price bracket?
It will depend on earning, depend on your credit and depend on your savings.......... so look at setting up TWO help to buy ISAs, as for every £200 you each save the Government will give you £50 which is a great opportunity to save your deposit you will need https://www.helptobuy.gov.uk/help-to-buy...
Do you have a deposit?
What's your credit score?
What's your annual income?
What's the value of the property you want to buy?