Need advice on notice period / gardening leave (UK, Big Tech)

I currently work for a big tech company in London and have been here for about 5.5 years. I’ve recently been approached by a competitor and I’m now going through their interview process (nearing the end)

I always thought my notice period was three months, but I’ve just realised it’s actually only one month according to my contract. If I were to resign and offer three months (e.g., to align with a potential start date), but my contractual notice is one month, can my company force me to stick to the one month?

Given that I’m moving to a competitor, I assume I’d likely be put on gardening leave anyway, but I’m unsure whether they can insist that my notice period is only the contractual minimum rather than what I request.

Any insight on how this typically works would be really helpful.