I don't know if you've seen it yet, but at the top of your screen in the website menu bar is "0 new PMs".  You can click that and (unless he deleted them) see any of Dave's private messages that he sent or received.  There might be relevant clues in those messages to help with your search.

Foul

If I might be so bold, I'd like to offer a suggestion.  But first, a story.

When I was little, I collected Hot Wheels toy cars.  They're like Matchbox cars which were initially created in England I believe.  Anyway, I saved them for decades and realized when I was 30 that they were somewhat valuable, around $300.00 for twenty cars and the case.  My wife saw them and suggested I let my two year old son play with them as I had when I was a boy.  I decided to sell my collection and buy more age appropriate toys for my son.  My wife was miffed.  I was not.  I had made a cold calculation.  That was my decision, but I understand not everyone would have done the same.

Now, onto your situation.  If indeed your husband had a "white box d&d set," there is a strong likelihood that it was a set of three rule books in a cardboard white box, about 6" x 9" x 1.5".   They were manufactured back in the mid-seventies.  These sets currently sell anywhere from $500 in poor condition to thousands of dollars if in excellent condition, if they are for sale at all.  It's a seller's market.

People have reprinted this set of D&D rulebooks, and these recent "Premium" reprints now sell for about $450 to $500 on eBay, it they are available.

There was a person by the name of Bill Barsh who was active on the forums, but he rarely if ever makes an appearance here now.  He's primarily on Facebook.  While I am a friend of Bill Barsh, and he would be somewhat sympathetic to your interest, I would predict he likely would not want to take a significant loss on its sale back to you, if he sold it back to you at all.  Again, these are difficult to come by.  He also lives in the US, so shipping back to UK would be expensive.  This is assuming that indeed Bill Barsh was the purchaser of your husband's white box set.

What I am trying to say is, you can probably find what you are looking for, but it could prove to be an expensive and challenging adventure.

There is another option.  It's WAY cheaper, but doesn't have the same emotional attachments of your husband's former set.  It's the same rules and game, but all in one handy, and new, paperback book.  It's for sale on Amazon at less than $5!  Here's a link to what I am talking about:

https://www.amazon.com/White-Box-Fantas ... 473&sr=8-1

My recommendation is this: buy the Amazon paperback versions for your sons, show it to them and then talk about whether you should chase after his original copy, or any original set.  With a set of dice, they can play the exact same game with the exact same rules that they played with their dad oh so long ago.  Is the sentiment you are wanting an experience or an item?  Or both?

Again, I hope you don't mind me being so forward.  My wife would be miffed at me for making this suggestion....  

Hi, if you decide not to take benjoshua's suggestion and still want the set of books from the 1970's please PM me. I have an extra set of the books. But I think benjoshua's suggestion is a good one.
Cheers,
Bill Meinhardt

Update!

I got to thinking that $4.30 was worth me checking out this product myself, so I bought a copy. It looked good! It was a Player's Handbook, Dungeon's Master's Guide and Monster Manual in one 144 page volume. It measures 8 1/2" x 5 1/2". The artwork was good, the layout was professional, and the writing clear. It's the kind of thing you can give a kid who is just learning about the game and you don't have to worry if they'll write in it, lose it, or tear it up. The last page is a character player sheet one can easily enlarge and copy.  The bottom line is that it's a really good product at an amazing price!  Below are some photos.  

Hi. I'm sorry for your loss. I've been reading the forums here since they began & remember Dave's posts were always friendly & encouraging in his interactions with other other collectors here.

As a suggestion regarding the Original D&D rules (White Box version): you can also get a PDF of it for $6.99 from DMs Guild. These are scans of the originals. They may help you decide if you want to get a hard copy.

OD&D Dungeons & Dragons Original Edition (0e) - Wizards of the Coast | D&D, Original Edition | Dungeon Masters Guild