What destination are you flying to? There’s a long-standing bug on ba.com where mixed class itineraries won’t be priced if a destination is served by multiple London airports. Try mixing ET and CE on a booking to GLA (served from LHR, LGW and LCY) and whatever you pick outbound will force inbound. Do the same for e.g. MAN (only served from LHR) and you can mix cabins.

The way around this is to book by phone and ask them to waive the call centre charge as the website won’t let you book.