What designs of lights are allowed?
When do I need to get a building regulation inspection?
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Depends on the distance from water. Homebase, of all people, have a good guide here.
In summary, lights in the bath must be 12V and completely waterproof (zone 0). If it's in reach of a bath (standing up or sitting down) your choices are limited to completely waterproof sealed units (rated IPX4) and you'll need a 30mA RCD (zone 1). Other areas at risk of splashing (Zone 3, including above sinks) need IPX4 splash-resistant fittings but don't need the RCD. Outside of that - in zone 3 - anything will do.
You may need to have the completed work inspected under Part P of the buildings regulations. Give buildings control at your local council a call - they can advise.