UKH

Front passenger door not opening of Honda Jazz. Issues with mechanism.

So panel needs to come off and replacement mechanism fitted. 

How much should this cost?

Presumably you mean the internal door card rather than the door skin. Shouldn't be more than 2H labour plus parts unless something very strange has gone wrong with it. No idea what Honda bits cost. Garage labour rates are very variable, get a couple of estimates if you're worried they're taking the micky.

jk

No idea, but take pictures of your tyres before leaving your vehicle with the garage.

Can't your breakdown cover company come and look at it?
We recently had the RAC release a stuck tailgate, actuator rod had come loose.

In case they substitute them?

https://www.ukhillwalking.com/forums/off_belay/how_was_this_damage_done_to_tir...