I had that same problem with my grandfathers record, both world wars. National Archive took me to its 'internet partner' ancestry.co.uk, which costs.
If you have access to ancestry, you may as well use it. They seem to be one of the very few doorways to the original records.
All this of course relies on the years your father was in service and if he survived the war he was involved in. If he unfortunately didn't he will be noted on the commonwealth war graves commission website. Contacting the British Army official site could also prove fruitful.