You could try asking for a credit limit increase. I do the same as you and my credit score is good to excellent. However my main credit card rarely goes above about a third of the limit. But that's because the limit is high, not because my spending is low, it's not, we average about £1.5-2k pm on the credit card, but this is just our normal spending and it's cleared every month.
Credit scores are fairly meaningless though, banks use their own systems to decide whether to lend you money and how much to charge you to do so.
Why not just use a debit card as the money that you're keeping in your account isn't earning any interest
If use of credit card is an alternative to overdraft use, it can save a lot of interest as the money stays in the current account longer, preventing overdraft use.
Also banks see use of overdraft as a bad thing, while regular use of a credit card that is paid off in full every month is a bad thing.
Plus there are numerous other benefits to using a credit card like purchase protection, cashback, cashflow management and it makes it simpler to manage your current account. Instead of having to monitor your balance and anticipate future direct debits to avoid spending the money needed, you just put everything on the credit card and it comes out in one lump a few weeks later and you can treat it like any other bill.