Jabra Pro 9465 Duo ticks those boxes (except cheap – they’re about £250).
DECT for base to headset (which is much better than BT for that), but can pair a mobile to the base over BT and pick up calls on headset. Plantronics Savi W720 is similar, at similar cost too.
Sennheiser DW Pro2 is another nice option but much the same price and no BT.
Logitech Dual H820e is also nice, and a bit cheaper – although still around the £150ish mark.
If you can live with corded for PC, then the Plantronics Blackwire 700 are quite a bit cheaper. They pair with a phone over BT and you can detach the cable below the in-line control box thing and use them for mobile calls while you wander about.