As other have mentioned the idea was already out there and other countries were already moving towards it with their designs. There's also the national prestige question. The Royal Navy had a reputation to keep up, and unlike with La Gloire where they could quickly answer with the much more advanced HMS Warrior here at best they'd merely be able to come up with something similar and look like they were following others so better to take the lead IMO. Plus with being able to build it in under a year thanks to building up a store or material and prefabricating parts before officially laying down the keel it also gave them the wow factor of coming out with something revolutionary and in such a short time.