I'm not entirely sure you'll get a similar sound. Those ATCs will have a scale all of their own. Not easy to replicate on a £2-3,000 budget. That said, you will get a sound you will find pleasing, assuming you know the qualities of the sound you like to hear, rather than the sound you have just now. I think it's fair to say that there's a difference.
What would I look at? For your budget? If you can land a pair of AVI DM5s, you'll get clarity and a soundstage you'll be surprised with. Alternatively, you'll maybe need to look at the likes of KEFs LSX II and a subwoofer. Then source gear to suit. I'm thinking a streamer in the first instance, but YMMV. All easily achievable under £3k.