You see that sometimes. It isn't common, but it does happen. A way to think about it is there being two different supply curves of deposits. It is usually reversed and larger deposits earn more. This is for two reasons. First, wealthier investors have less tendency to let inertia determine where their accounts are and so are willing to more elastically supply funds and the variable costs of adding a single account are independent of the size of the account.
However, there are environments where banking accounts are the single best investment option possible. In that case, those large deposits cannot flee into the bond or stock markets. Furthermore, the banks may be desirous to reduce their deposit levels, but not lose their customer base. This would encourage wealthier depositors to consume their money rather than deposit it. Banks may want to reach target funding levels that are slightly lower than their current level.
Finally, certain types of assets can imply certain preferred types of deposits. For example, banks that offer a significant number of lines of credit, letters of credit or other forms of contingent funding usually carry a lot of demand deposits and fewer long term deposits. Conversely, banks that carry longer term loans tend to carry longer term deposits. The mix of banks assets may be changing.
Finally, Brexit will probably crush British commerce and if banking is preparing for this, they may be shortening their asset base and in doing so trying to shorten their deposit base to be flexible in the event that Brexit is as catastrophic as it could be.
The Port of London is huge because the Industrial Revolution began there and so outflowing trade required it, but as other nations joined the process it became natural to use London as the nexus of trade between the Old World and the New World. When the European customs union came into existence this substantially reduced the competitive value of ports such as Antwerp. If customs duties are now present, it is unimaginable that customers selling to Europe from North or South America would even consider shipping through London to Europe, if the principal European ports were large enough to handle the traffic. Because of history, they are not yet, but when they become so all the supporting commerce such as warehouses, banks, trucking companies and makers of intermediate goods for final shipment to Europe should get crushed.
Banks may be getting ready.