Are 36 spoked wheels really necessary instead of 32 spokes

I would say so. I prefer 36 myself, but that's purely my own idiosyncratic preference and if it came to it, I wouldn't hesitate a second to go for some light touring on 32-spoke rims. You'll be fine.

32H wheels will be fine.

A set of 32 spoke hand built wheels, built properly and well, are more than strong enough for touring. Mine have certainly carried a lot of weight including me over the years in various trips from heavy shopping to a loaded tour.

However you might have problems if they are FACTORY built 32 hole wheels as spokes will break. Of the factory built wheels that have been supplied on bikes that I have bought over the years every one has soon had spokes break. The only solution was to rebuild the whole wheel with DB DT stainless steel spokes and plain spokes on the drive side for added strength. Not a single problem since.

Enjoy your tour of East Anglia.

Edit: Just read andymiller's post above. If I were riding into the back of beyond with a heavy load I would go for 36 hole wheels for added strength and peace of mind, maybe even 40 hole rims, but for smooth road touring in UK and Europe it is not really necessary.

With 36 spokes, if one breaks you can generally ignore it and carry on riding unless it's threatening to tangle with the rear mech.
With 32, you would probably have to undo the brake release on that wheel or adjust other spokes to get rid of the wobble.

If you've not fiddled with the other spokes, it's generally adequate to just put a new spoke in and tighten it to the same tension as the adjacent spokes on that flange. If you have adjusted other spokes to straighten the wheel enough to use the brakes, a much more involved retruing job will be needed.

A well built 32 spoke wheel is strong enough that any problems would be unlikely.

The 32 vs 36 hole issue w.r.t. touring has been bugging of late. For I have been oblivious to the accepted/conventional wisdom of the advantage/necessity of 36 holes for touring wheels until very recently. In the past 3 years I've done three light load week long tours (no tent) and one fully loaded weekend bash Leicester-Bristol-Leicester on 32 hole hand built wheels without any issues. Indeed further, again oblivious to the conventional and accepted wisdom, I've over the past 18 years built all my 32 hole wheels 2 cross with no issues. The only time I had a spoke break was on my 28 holes wheelset where 2 cross is the accepted norm. I can only think that rider weight (I'm 5'7" and medium weight) and build quality are factors.

Of course as a cyclist I am aware of Brecht's advice 'He who laughs last has not heard the bad news' - i.e. I break a rear spoke on my next tour when it is raining and cold.