If British inflation is higher than U.S. inflation, fewer U.S. people will want to buy British products, because they will have become comparatively more expensive than U.S. made products. This will lead to a decreased demand for the British pound sterling on currency markets, which will lead to a depreciation of the British pound sterling.
If U.S. income levels improve relative to British income levels, people in the U.S. will be able to buy more British imports. The increased demand for the British pound sterling (to pay for the British imports) will cause the pound to appreciate, not depreciate.
A decrease in the outflows of British capital to the U.S. will cause a lower level of supply of British pounds. This lower supply of British pounds will cause the British pound to appreciate.
If British interest rates rise, more people will want to purchase investments denominated in British pounds. Therefore, the higher demand for British pounds will lead to the appreciation of the British pound.
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