Are you sure that the deregulation is not just empty word?

Yes, you can usually pick your own retailer for you utilities. But you cannot pick the distributor (downstream of the retailer, owns cables or pipes in your street) or transmission (upstream of the retailer, owns the cables or pipes providing your city).

The sales/distribution company usually doesn't own anything, they are just sales and marketing office. Everything is physically provided by companies, that you cannot choose.

No, but the sales balance on the National Grid is still based on competition, because it is regulated by the interaction of dozens of companies. The distributor has no control over who generates power, or how much is paid for it, and that is why there is no shortage [1].

With non-power utilities, even this isn't an issue - water or gas are never randomly shut off without warning.

[1] There is a small deficit of generation capacity under some conditions, primarily due to recent underinvestment in nuclear energy, so power is purchased from France routinely, who have a large surplus due to their much stronger generation infrastructure, but even if this became unavailable, the capacity is enough to prevent US-style grid failures.