It sounds like your father began in military service in the Royal West Kents but then applied for service in the Recce Regiment – it was a selection process and one was required to pass the Selection Course. Posting his Army Number will help. Army Numbers were allocated in batches to different Regiments. If he is from the RWK batch then that will show that he started his military service there.
As for working out which Recce Regiment he was in, you will need his Service Record. Go to http://www.gov.uk and type in ‘Military Service Record’ and follow the directions. Do not worry if you do not have all the information that they are asking for.
Each Division in Italy had a Recce Regiment so only the Service Record will pin it down.