Assuming that both the United States and the United Kingdom allow their currencies to float, the situation you describe will lead (all other things being equal) to a decrease in the price of the dollar when that price is stated in pounds.
When there is an increase in American demand for the pound, people want to use their dollars to buy pounds. When this happens, the supply of dollars that are available to British people goes up. The law of supply tells us that whenever the supply of a good or service goes up, the price of that good or service will (all other things being equal) go down. Therefore, the price of the dollar (expressed in pounds) will go down in this situation.
The demand for one country’s currency will have an impact on the other country’s currency, assuming normal economic circumstances. Thus, if the American demand for British pounds increases, the price of the US dollar will drop. This will occur because as the demand for a country’s currency rises, it makes that currency more expensive. Americans would have to spend more US dollars to get the British pounds. This means there will be more US dollars floating around, creating an oversupply of US dollars. As a result, the price of the US dollar would drop.
The laws of supply and demand apply to international financial markets as well as to the market for goods and services. Increased supply will lower prices while increased demand will raise them, with all factors being equal.