Simple answer is that as long as the garage you choose is a VAT registered garage and services the vehicle in accordance with the manufacturer's specifications then you are perfectly OK and are still covered by manufacturer's warranty.
Google "Block Exemption Regulation" for the finer details and any gotchas.
Regarding servicing under manufacturer's warranty then the "Block Exemption" rules still apply but I have not researched the finer details as to whether "only manufacturer's approved parts, if stated" could, in the event of a warranty claim. e.g you have had a Mahle oil filter fitted and not a Fiat/Lancia fitted, result in an issue. I doubt this would be an issue but I have no proof either way.
My gut feel is that any reputable OEM/equivalent quality part although not carrying a Fiat stamp or sourced from Fiat (MOPAR ..... Marelli ..... etc) will be deemed by the courts to be OK and perfectly acceptable in fulfilling manufacturer's specifications/requirements.