Should I study classics and ancient history?Watch
Generally business (and finance) roles in the UK/US/similar will accept any degree background to go into, except some roles which may prefer/require a numerate background (e.g. from pursuing a STEM subject). However the vast majority will accept any degree background, and if they have any preference it's usually regarding where you get your degree rather than what you get it in. Thus a Classics background is acceptable for the majority of graduate roles in the business realm anyway (especially if you go to e.g. Oxbridge/UCL or similar...).
As above though, it isn't an easy degree (although most employers are likely to recognise this and may consider that favourably) but as with any course you're actually interested in and/or able and willing to engage with, it's undoubtedly rewarding in itself.