I would consider the HEDD Tower Mains with one of the woofer sections, if you could get a slight discount off the MSRP, which should be possible, since they are about £800 over your 12k budget. Then buy a quality blue tooth receiver like this:
https://www.whathifi.com/us/arcam/rblink/review
Not wireless but: https://www.stereophile.com/content/dutch-dutch-8c-active-loudspeaker-system
I grabbed a pair of Meridian DSP8000’s used, unbelievable how affordable they are compared to separates.
I would consider the HEDD Tower Mains with one of the woofer sections, if you could get a slight discount off the MSRP, which should be possible, since they are about £800 over your 12k budget. Then buy a quality blue tooth receiver like this:
https://www.whathifi.com/us/arcam/rblink/review