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How to make an erc20 token that tries to mimick the pound value and track the dollar to pound value ratio?

So if it goes up to 1 pound is 1.40 dollars I want to automatically buy/sell to match this value ratio, same when it drops to 1 pound is 1.20 dollars I want to automatically buy/sell to match this value ratio as well.

I know there is tether and BUSD to match for the dollar value, but how do I track the pound value inside ethereum (or binance smart chain) reliably, and how to lose as little fees as possible for the swaps

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In order to get the pound value in your ERC20 contract, you would need to use some Oracles like Chainlink.

Building decentralized stablecoins is complex. There are 2 approaches that you can borrow from:

  1. Rebasing: The supply of tokens increases/decreases to maintain peg. Eg: AMPL
    Many projects have failed as the tokens continue to lose peg and get caught in a death spiral.
  2. Collateralized: User needs to deposit collateral like ETH, etc. in order to mint the stablecoins. Such type of stablecoins are more successful as the token can always be redeemed for collateral and value is not created out of thin air as is the case with Rebasing tokens. Eg: DAI, LUSD

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