Hi blodwyn,
Crickhowell and Narberth (!) are miles away from each other. Crickhowell as you say in Brecon and Narberth in Pembroke.
There must be a good reason for you to be told to look there. Can you elaborate?
Ashford is not a common name in Wales, the the chances of you finding him are relatively good. The best place to start is on the LDS site, with the 81 census. I had a look there, entering only his name and Wales as place of birth. You are in luck - there is a grand total of 1 entry for this name. Sorry I can't copy the info, but if you look, he's there in Denbigh, living with his brother Thomas and sister Sarah H., all 3 born in Begelly, Pembs.
My next suggestion would be to look at the 71 census on ancestry for these names - the chances are that Sarah will still be living with her parents.
Following that, look for Alfred and Thomas with their parents in Begelly in the 1851 census.
If you look at the freebmd site (sorry I can't from work - the site is blocked) you may well find their births, and knowing their parents names from the 51 census, you can order not only their birth certificates, but also their parents marriage cert. THAT will give you the names of Alfred pat. grandfather at least.
Good luck
D ap D