the thing leading to the outside tap is a stopcock. Observe its unique sloping shoulder (a stopcock is designed so it will turn off the supply even if the washer is perished, or falls off, and might last a hundred years). This one you will see is bigger at the incoming side, a good sign, as it means you have a larger incoming pipe and can increase the size of your stopcock and internal pipes for improved flow. Sometimes the stopcock has the pipe size moulded into it, in mm or in inch fractions.
But your outside tap one is not for the whole house, it will typically be under the sink, or under the hall floor. Sometimes there are two or more of them in the house, for example where one has seized or has been walled up by a kitchen fitter so it is no longer accessible (this is very tiresome)
There may also be some little ball valves like this They are almost invariably of very poor quality (observe the price). Not only will they leak for no particular reason, they have a very small aperture inside which obstructs water flow and can become noisy. If you have any of these they should be replaced with full-bore valves such as these which are ten times the price and a hundred times as good. The T-handle ones are fairly small and neat and can be operated without tools. As they are generally full-bore they do not obstruct flow, which is important when you need good flow from an unvented cylinder or combi.
Can you guess which ones economy-minded plumbers usually fit?
The colour and material if the supply pipe is important. In a very old house it may be lead or iron, which will be liable to leak due to age. Or it may be copper in a small and restictive size. Or it may be black or blue plastic, which tends to give better flow as it is probably free of connectors or elbows, and may be in a bigger size.
A 1950's house probably has a half-inch-internal copper pipe, which is more or less adequate but not designed for a generous flow. If you can measure it, the external diameter is about 15mm. It can be an advantage to dig a trench out to the pavement a lay a new, larger plastic pipe. People who do this are often astonished at the improvement and delighted at the performance of their unvented cylinder.