The embassy probably doesn't know whether your father had Dutch nationality when you were born, since the circumstances governing this could include any of several things that they wouldn't have known about. The best way, and the way the Dutch government would go about it, would be to investigate the relevant points in his life.
Before doing that, though, you might want to check whether it matters. This is because even if he was Dutch when you were born, he might not have passed that nationality on to you, or you might have lost your Dutch nationality since then. (If you are formerly Dutch, though, this could be useful to know, as it is somewhat easier to regain Dutch nationality than it is to get it for the first time.)
Since the rules have changed over the years, it's impossible to say exactly what circumstances matter. These depend principally on when he was born and when you were born. Likely things to look into include:
- When and where he was born
- His parents' nationality
- Whether his parents were married
- Whether he ever naturalized in another country and, if so, when, and, if before he reached the age of majority, whether (and when) his parents naturalized
- Whether he lived outside the Netherlands for a period of 10 years or more after reaching the age of majority, and, if so, where
If you want to edit your question to add some detail, leave a comment on this answer to alert me so I can address it.
Another option is simply to apply for the passport, claiming that your father was Dutch and that you are Dutch. This would require the government to make a determination about his nationality when you were born and whether he passed it to you. Of course, it would be best to have a good understanding of the law before trying to do this.
You can also of course ask a lawyer, but I have to say that I had a bad experience with a well known Dutch immigration law firm, and I have since seen an incorrect analysis of Dutch nationality law on their web site. If you are up to working through it all yourself, you're probably better off saving your money.
With regard to your edit:
First, since you were born in 1987, you might have lost your Dutch nationality on your 28th birthday in 2015. If you've lived in the EU, though, you might be okay, since that is one of the exceptions to the ten-year rule. The exception seems to have been added with the 2003 changes.
Second, I think you are probably right that your father would have lost his Dutch nationality unless he received an official acknowledgement of his Dutch nationality. Indeed, this must have been done in the ten years before you were born, and every ten years before that, except that it was not necessary before he reached the age of majority, or while he was living in the Netherlands (I assume your father moved with his father to the Netherlands after the war and back to the UK in 1969).
I have forgotten when the age of majority was lowered from 21 to 18, but if he never received an official document confirming his Dutch nationality he would have lost that nationality sometime between 1979, ten years after moving to the UK, and 1980 (his 31st birthday).
If your father ever received such a document, there would have been a new ten-year period from the date of the document. So if he got a Dutch passport or consular statement of nationality before the date in 1977 that fell ten years before your birth, he would have needed to have a second one after then to have retained his Dutch nationality until your birth. If he got a document between 1977 and 1979 or 1980 then you only need to have evidence of the one document.
There is one caveat here: The law changed a few times, at least once altering the 10-year rule. In a later form, for example, the rule only applied when the person lived in the country of birth and had the nationality of that country (which of course also applies to your father). So to know for sure whether your father lost his Dutch nationality under that rule, it's necessary to know the precise form the rule took in 1967 (the year of his 18th birthday) and any changes that occurred between then and 1987 (the year of your birth).
If the Dutch mission to the UK ever issued a passport or certificate of Dutch nationality to your father, there should be a record of that. I do not know whether such records would be available through some sort of freedom-of-information request.