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If I loose a £1 coin I loose a £1 but does the Government win?
Yes, but not the whole £1, and it's the bank of issue which wins. In England as in most countries, the sole bank of issue is nationalised and the currency is fiat issue with the seignorage accruing to the national exchequer.
Assuming the coin is permanently lost or destroyed, the mint makes another one which costs a few pence and sends it to the bank of issue, which then puts it into circulation by buying commercial or government paper. The bank now has the paper it bought with the original £1 and the paper it bought with the replacement £1. There has been no increase in the money supply, so the new coin doesn't generate inflation. The profit to the treasury is the difference between the face value of the coin and the cost of manufacturing and issuing it.
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gbj_tester
If I loose a £1 coin I loose a £1 but does the Government win?
I can remember when notes used to say “I promise to pay the bearer the sum of £1” so I guess the Exchequer wins if this promise is removed but it can’t work out why.