Welcome to AiX wntic.
During World War 1, this area was a Royal Naval Airship Station and, as such, would have stores relatively small amounts of aerial bombs usually in the 20 pound weight range and small arms ammunition. The station closed after WW1 and came back into use in the 1930s for the development of the commercial airship R101 but was closed before WW2.
With the close proximity of RAF Breighton to the northwest it is possible - but unlikley - that immediately post-war that the Howden site was used for the temporary surface storage of surplus aerial bombs prior to final disposal. Usually - for RAF munitions - redundant airfields were used for this purpose since they were already under Air Ministry control.
That leaves, then, possible use by the military (Army). There was already an RAOC Depot at Baralow (6 miles to the southwest) so this is unlikely.
In any case, it was incumbent for the RAF and Army to carry out a formal search of the areas within their boundaries using Bomb Disposal teams before handover of the land to the previous owner. A certificate of 'free from explosives' was recorded at and issued from the Air Ministry or War Department and this covered a search and disposal to a maximum depth of 2 feet.
We then consider any bombs dropped through enemy action or allied accident during either world wars and whether they were dealt with at the time or recorded as low risk and low priority.
Reasonably, a developer has to consider the risk that any unknown unexploded munitions may pose and follow guidelines such as:
I should have thought that Yorkshire County Records Office would have information of any post war military use of the Howden field.