A shower is supposed to be much more energy efficient than a bath. It uses less water and less gas/electricity. A shower might use as little as 20 litres of water on average, and a bath might use 150 litres. In addition, many showers use shower units. The water is heated as it is used, and not pre heated and stored in a hot water tank. Often as a consequence, the whole central heating system, including radiators and pipes, is also heated and this is wasteful.
Even ignoring these sources of inefficiency, a bath might cost 90p. A shower might cost a third of that and even as low as 10p using a aerating shower head which mixes air and water - air has a low heat capacity so it does not take much energy to heat. Using a shower head like this produces a spray, meaning that a large area can be washed in the same time. With a typical saving of 60p per day per person, a family of four can save £2.40 a day, or £16.80 per week, or £873.60 per year. This is maybe a quarter of a their energy bill.