European leaders can't "force" the UK to take a quota of refugees from elsewhere in the EU, or anywhere else for that matter.
The reported EU proposal to relocate 120,000 asylum seekers from countries like Hungary, Greece and Italy appears to be on top of a plan first floated in May this year, which sought to distribute 40,000 people among other member states. This explains the reference to 160,000 by the Express.
Such a scheme might compel most member states to accept more asylum seekers, but the UK is an exception. We have what's often referred to as an opt-out, although strictly speaking what happens is that EU laws on the likes of asylum and border control don't apply to the UK unless we choose to opt in.
The European Commission acknowledged as much in its proposals in May, and again in its more recent proposals.
It left the UK out of its calculations for what it considered a fair scheme for relocating asylum seekers within the EU, and similarly seemed to accept that Britain couldn't be forced to resettle people from outside the EU either.