Shouldn't need a whole new engine.
Even if valves have met pistons, these engines are rather clever in having sacrificial rockers that break saving the valves from damage, put the timing right preferably with a new chain and tentioner kit which isn't very expensive, and replace any broken rockers which are inexpensive, and you're good to go.
A replacement engine is likely to cost £500 - £1000; when factoring in labour costs, new clutch (which you'd e stupid not to do while the engine is out) and any parts that get damaged or need replacement, such as clips, nuts and bolts finally a full service of the new engine, assuming you don't know when it was last serviced. All this makes it most likely uneconomical to repair
Where as...
Complete set of rockers £120
https://www.ebay.co.uk/itm/Fiat-1-3-JTD-Multijet-Diesel-Set-of-16-Rocker-arms-Lifters-cover-gasket/112587625325?hash=item1a36bed36d:g:jwgAAOSwK89Z04bX
Complete timing chain and cam locking tools £85
https://www.ebay.co.uk/itm/ALFA-ROMEO-MITO-1-3-JTD-JTDM-MULTIJET-DIESEL-TIMING-CHAIN-KIT-LOCKING-TOOLS/302343742888?epid=685323709&hash=item46651765a8:g:m6oAAOSwHjNV9CGV
Cost of labour far less than an all out engine replacement, the car keeps the right engine and you know all the history.