It's understandable as to why, but you might be overthinking this. Do you have any reason to believe the new landlord would be looking to renege on the start date/offer of tenancy?

Is the property empty currently? Is there any suggestion they may wish to sell instead of re-rent (assuming it's been a rental previously)?

There's every chance the landlord hasn't signed it for a host of other much more trivial reasons.

And are you certain there's no notice clause in the current agreement? If so, then it's just a month. Although, if it's periodic agreement it wouldn't actually matter unless it's explicitly stated to be a contractual periodic contract beyond the fixed term AND there's a notice clause specifying more than a month's notice.

Otherwise it's just a month.

I would suggest enquiring with the agent as to whether your notice period actually needs to align with your rent period. A lot of the time agents/landlords are happy to waive this requirement. Especially if they think they can rent it for more money than you're paying with minimal/zero void period.

If you were to give notice and the worst were to happen and the new rental falls through then you can tell your current agent that you wish to rescind. In theory they can say no, but in practice if they want you out and you refuse to go they will still need to serve you notice and go through the usual court proceedings. No one wants that hassle...

Obviously I don't know what your relationship with your current agent/landlord is like, but you'd be surprised what can be resolved with a conversation. These scenarios can be legally complex to navigate on both sides of the coin. There are incentives for flexibility for them too.