You won't find his enlistment online unless he was in one of the smaller Corps or REME, which have so far had their
records processed by the National Archives, with some of those being available on Ancestry. The remainder of the 9 million records which have recently been transferred from the MOD to the National Archives are in the process of being catalogued.
You have two choices. Either wait until around 2029 when TNA expect to have completed the task, or contact the MOD with the details you have and ask them to provide a reference number which you can present to TNA in order that they can locate and copy his service documents.
https://www.gov.uk/get-copy-military-records-of-service/apply-for-the-records-of-a-deceased-servicepersonUnfortunately just asking TNA to find an Alfred Smith born 1917 will be an unrealistic task (see below) until they have indexed all the records. The MOD on the other hand already have a partial index which should allow them to find the relevant person. You won't need to provide a death certificate as it is obvious that Alfred will no longer be alive.
Incidentally just to give you an idea of the problem, there were 623 Alfred Smiths born in 1917 in England and Wales alone. After we add in Scotland and Northern Ireland that figure might be around 750. If we guess that around 500 of these went on to serve during WW2, with around 350 joining the Army, 100 going into the RAF and a further 50 to the Navy, you can see the extent of the problem. In 1942 the size of the British Army was 2,438,000 of whom around 140,000 were in North Africa.
Good luck with your quest.
