I am pretty sure that the UK will accept a youth mobilty deal with EU. There will be some give-and-take, since the EU proposal was maximalist (maybe a - high - cap), but the essence is that UK needs this more than we. Also: a youth mobiliy scheme is popular in UK.

What the UK wants is better tourist travel and trade deals. Youth freedom to roam is not important & potentially electorally damaging

And I am pretty sure it will be bundled into a wider agreement with some stuff the wider public want