As other posters have pointed out, banks require applicants to demonstrate repayment capacity for the proposed mortgage over the last 6 months, i.e. you need to show that you have been living as if you already have the mortgage that you are applying for (to varying degrees - with some banks, the target is the actual proposed repayment, whereas some others set the target at the stressed repayment, i.e. current rate + 2%). Every bank will take into account savings that you have built up in your current account, or that you are transferring to other accounts (for which you can provide statements), as long as the overall build-up in your funds is coming directly from income from employment (i.e. not one-off lump sums or just moving money around). If you have definitely been demonstrating this over the last 6 months, then the person you spoke to in the bank doesn't know their job properly, or they have not been provided with sufficient proof, i.e. statements.
Quite apart from savings, your current living situation might cover this requirement on its own, i.e. if you are renting or paying a mortgage right now, then that payment/repayment can be offset against the target for repayment capacity.
Best regards,
Dave Curry CFP®
https://www.linkedin.com/in/davecurryirl