Hi, OP -
I am a former admissions tutor in a (Russell Group) maths intensive STEM School. Pedagogically, Data Science is a hybrid of Maths, Stats and CS with emphasis varying by degree programme. In that sense, a good Joint Hons programme in Maths and Stats incorporates much or most of the formal knowledge of a Data Science degree. Learning Data Science after the Bath degree would be largely a question of learning how to apply what you know, while also giving other options for the future.
Not difficult to pursue Data Science, the hottest option, in theory.
However the reality can be different.
A good Data Science programme will emphasise particular areas of Maths and I would expect it to have more CS than a Maths and Stats programme. It sounds more specific, and hence more limiting, superficially; however the mix of modules, particularly at a top university like LSE, should offer a good amount of transferable skills. I admit I was biased against the Data Science degree for a while, particularly at the UG level, but am no longer as I am seeing how it plays out.
This is a rare case I would not decide based on the merits of the degree programmes, because both are excellent. However there are significant differences. Then there are the very different universities and cities, wonderful in their own ways. These affect the university experience significantly.
IMO DC should choose the one where they can see themselves engaging most fully. That is likely to lead to their greatest success and give the most options for the next stage of life.
Best wishes to them.