I suspect the timing of consequences may be different in the US and UK, so that may influence how much weight you should give to answers from Americans. However … my son was, and remains, scary smart by certain limited measures. For whatever reason (gifted kids are often lazy as a result of not being challenged, it seems) he had a tendency not to work hard - if he understood something instantly, great; if not and he had to work hard at it, he instantly thought it was “too hard” and he’d never be good at it, so why bother?
As you can imagine, this was not a great recipe for an outstanding high school record, though certainly a recipe for a decent one. I was fairly hands-off about most of it (disclaimer: a careful search of my posting history would reveal I basically went nuts over the college admission process). One of my child-rearing mantras had always been “actions have consequences” so I left it to him to act and discover what those consequences might be. I did quite often remind him that, “things are easy now, but just be prepared - even smart people have to work hard to learn advanced things. Hopefully you’ll being studying advanced materials in areas that you love so you’ll want to do it - but make no mistake, a day will come when you DO have to work hard.” I think I said that enough times for it to sink in!
His dad was a bit more hands-on than me; not insanely overbearing, but likely to give a lecture if he saw sloppy homework or a test score that clearly didn’t reflect capability. It was probably good for our son to get a little of both types of parenting.
So where are we today? Well, CairoSon had his heart set on Cal Tech or MIT, with Harvey Mudd as a decent alternative. All three schools rejected him. He went on to a well-regarded SLAC, but not where he had wanted to go, and has done great (except for being apparently incapable of scheduling himself for the GREs, which may turn out to be a huge problem; I just posted the story in MPSIMS). In fact, with the important exception of his GRE scheduling, he’s amassed a pretty spectacular record.
My take on all of it is - in-born temperament is likely to persist no matter what. I was disciplined to the point of being hit for performing anything less than fantastically well in school, and it had zero impact on my performance except to make me anxious and resentful. But somewhere around my junior year of college, I magically on my own transformed into a very serious student - because I had matured to that stage emotionally on my own.
Again, the US and UK systems are different, and the US system is ultimately pretty forgiving, I think; a poor student who is smart can rectify their lousy performance later if they are willing to work super hard. I don’t know if that is the case for your daughter. But, unless she will irrevocably and horribly screw up her life unless you terrorize her into a higher level of performance, I’d say, based on my own and my son’s performance, let her be in charge.
(Come to think of it, I think my son’s dad’s story points in the same direction: we are three for three on “smart but didn’t work to capacity in school.” When he went to college, he immediately became a workaholic, and he has never looked back.)
Also, if she dislikes maths it doesn’t matter if she’s got aptitude for it, it would be a terrible area for her to pursue career-wise. Not only will she be unhappy, she’ll eventually be out-performed by people of similar talent who love what they are doing and thus will go an extra mile.