Why do banks offer less interest on larger deposits? This may be a UK only thing but...

I have noticed that it is very common to see current accounts that offer some interest on the first couple of thousand pounds deposited with them and then less interest on sums over that amount. Why is this so? Surely they should offer more interest due to economies of scale.

Examples: 

Starling bank 0.5% up to 2,000 - 0.25% above

Nationwide FlexDirect 1% up to 2,500 - 0% over 2,500

Tesco current account 3% up to 3,000 - 0% above
When you lend your money to a bank (by depositing it), they don't just make money off of lending out your money. They also make money out of charging you for banking services. If the bank makes more money off of offering you services then they can afford to pay you a higher rate of interest (all other things equal). Check out: How do banks make money? The fallacies of fee income (Rice and DeYoung (2004)) 


  But banks also earn substantial amounts of noninterest income by
  charging their customers fees in exchange for a variety of financial
  services. Many of these financial services are traditional banking
  services: transaction services like checking and cash management;
  safe-keeping services like insured deposit accounts and safety deposit
  boxes; investment services like trust accounts and long-run
  certificates of deposit (CDs); and insurance services like annuity
  contracts. In other traditional areas of banking-such as consumer
  lending and retail payments—the wide-spread application of new
  financial processes and pricing methods is generating increased
  amounts of fee income for many banks.... Remarkably, noninterest income now 
  accounts for nearly half of all operating income generated by U.S. commercial  banks.


If spending on banking services increases more slowly than account balances and the sums involved don't make it worth the trouble of having multiple accounts then banks will be willing to offer higher rates on smaller balances. But, empirically, my impression is that this is atypical. It is more common to see higher rates on higher balances, because the transaction costs on serving one \$100k account are smaller than those of 10 \$10k accounts, and so they can pass some of those economies along as higher rates.