Yes, you can. Firstly, the property will need to be mortgageable without retentions, so you will usually be choosing a good condition property. Then your financial adviser will need to direct you to a lender that can process your application and issue a mortgage offer within the short time scale available before the auction. You will need to have your mortgage in place and your mortgage offer to hand when you bid in the auction room, that’s because if you are successful you will exchange contracts on the fall of the hammer and will want to have your funding guaranteed so that it is available for completion.
There is an alternative and that is specialist auction finance; it can be more expensive but can be organised very quickly to help fund your purchase in the interim while a mortgage is arranged. It is very important to do your research beforehand, and don’t be tempted to bid if you haven’t sourced your funds and had their availability confirmed.