In theory, it is true that under a fixed system when the £ ought to appreciate, the UK government could print an infinite amount of £ to sell, which they could then use to keep on building up their $ reserve. However, this would lead to a corresponding increase in the money supply and lower the interest rate. Ultimately, this is likely to lead to inflation, which would in turn then remove the excess demand for £s and hence the upward pressure on the £.
In principle, if you have complete control over capital flows into and out of your country/currency then you do not need to have a foreign currency reserve. However, you may hold such reserves in anticipation of the time when you relax capital controls, as will probably start to happen with China in the near future, as it becomes more integrated into the international financial system. Equally, there may be other strategic and political reasons for holding foreign currency reserves.
I think the answer to your final question is true. Typically, a fixed exchange rate can help to keep your inflation rate low if you fix your exchange rate to that of a low-inflation economy. This is because if your inflation exceeds that in the low-inflation economy, then the pressure is on your currency to depreciate and so you will need high interest rates to protect your currency, which in turn will tend to reduce inflation (down to the rate in the low-inflation country).
Conversely, if your inflation is less than that in the other economy, then the pressure is on your currency to appreciate. So you will need lower interest rates to prevent your currency appreciating, which in turn will tend to increase inflation (up to the rate in the other country).