Well the good thing is that you do have this cushion for unexpected expenses. If you didn't have those savings, presumably you'd have to borrow to cover them. Frustrating when what you want to do is build up your savings, though!
One of the things that really made sense to me when I first started using the budgeting tool YNAB was 'know your true expenses'. A lot of unexpected expenses aren't actually unexpected, they're variable and unpredictable, like car repairs or one-off prescription costs, or even down to needing new shoes. Knowing your true expenses takes time and is more than looking at just the monthly direct debits. I then put money away into those categories every month and let it roll over until needed. So I have categories for clothing, car repairs, Christmas, insurance, holidays, birthdays, household repairs, and an emergency fund - and then when I have to buy something in one of those categories, usually the money is already there for it.
I appreciate, though, this is far easier said than done in the current climate, but it's definitely worth looking beyond the predictable monthly expenses and putting even small amounts away to manage the unpredictable, non-monthly expenses when they arise. YNAB is a great tool to do that but it does cost money, you could do something similar with a spreadsheet and some bank accounts support the idea of savings pots, so you can put money into a pot labelled car repair, for example.