The speakers are clearly the limiting factor, as they are budget/mini system level. We don’t have a budget but here goes.
Some of the speaker suggestions are somewhat ‘aspirational’, given the rest of the system, but the basic truth is you need to match the quality of the speakers to the quality of the amp and the room, and to some extent the source too.
It sounds like you need some ‘fairly decent’ bookshelf speakers. They can’t be too revealing/good as they’ll expose the shortcomings upstream (source and amp) but they need to be ‘as good as you can get away with’. B&Ws are solid and get good reviews but I’ve never been a massive fan of them myself. Rega also have a good rep and could be a good bet s/hand. Dynaudio are very good, IMO (Audience 42s for example) but without knowing your particular amp they may be a stretch as they need some driving.
I’d see what Richer Sounds have in your budget for Mordaunt Short (low budget, don’t write them off), then Wharfedale, Fyne, Dali and Acoustic Energy (mid-budget).