My Vaillant system claims to do that, but it doesn't have dynamic input of pricing so you have to type it in on the head unit. I'm not sure it's even possible to get an API for dynamic pricing of UK energy prices.
There's a (third-party?) dashboard of the data here: https://agile.octopushome.net/dashboard
Does make it very clear where the afternoon peak is though, and that's a nice dashboard.