Not a silly question at all.
What is the fuse/breaker and cable protecting this circuit? I imagine it will either be a 20A and a radial circuit to the grid switch, which then feeds the separate points, or a 32A Ring Final Circuit to the grid switch, with spurs from each isolation switch. It might also be a radial in 4mm Twin and earth, with a 32A breaker.
What do you plan to plug into this new socket? Is it likely to be high load appliances, or just low power items?
If it's a 20A protected circuit, then adding another socket with no changes to protection/grid switch would in theory be fine, except that the circuit might be at risk of overload in normal usage, if the tumble drier and washing machine are both on at the same time - and depending on what the new socket will be used for.
If it's a Ring Final Circuit to the grid switch, then you could either:
1. Add a new grid switch at the grid, which feeds just the new socket you want
2. Add a Fuse either at the grid switch or as an FCU anywhere before the new socket, so that you are in effect creating a fused spur, which can have multiple sockets. Again, some consideration should be given to whatever the loading will be as it is not good practise to load an FCU regularly at close to (or even slightly more than) its rating for any length of time - that is a recipe for melted contacts, though a quality FCU helps.