what time should my 8 month old Shih Tzu have his last meal?

When you say 'cut quite short' do you mean someone used clippers on him? That can irritate if cut too short.
Wait a few days for the hair to grow back a bit. If he continues to scratch then check the skin isn't red and angry.

I once had a Shih Tzu that started this at the same age almost exactly. The vet said difficult to say if food related allergy or contact related eg shampoo, etc. in the end I found it was his food. He was on Royal Canin which was just too strong for him. Changed him to an anti allergenic salmon based dry food. This was left out all day so he could graze. After we ate (7ish) he was fed his dinner ie half a small carton of wet dog food such as Caesar. This regime did the trick.

He shouldn't be seeing in the house at this age. I had a cat flap fitted so dog could take himself out if need be.

Weeing not seeing....

The irritation could be diet-related, and maybe urine is too strong. I always feed my dog at 5pm (not aways possible if people are at work) and keep her water bowl full. Domestic dogs are not now regarded as pack animals, but family members, and don't have to be fed last. The dominant-submissive theory has been dismissed (thank goodness - those sorrwful eyes watching every mouthful whilst we were eating and he wasn't!). Baby wipes for sensitive skin, containing aloe vera, are great for dogs' eyes and sensitive bits, if urine is irritating.

I changed my dog over from Royal Canin to Iams, because it was too rich, irritated her mouth and gave her the runs. If the irritation stops, he will have better bladder control seasider.

Dry dog food can cause urinary problems in some dogs. The itching and soreness may be signs of an infection. I would try switching to wet food for a while and see if it helps. You would need to do it gradually over a few days, to avoid him getting diarrhoea. Don't want another problem!

thanks everyone I will try some different types of food. It may just a coincidence that it happened at the same time as his first very short hair cut but I did wonder if it was a sort of shaving rash!. We hope to eventually have a dog flap fitted but our house was originally two flats and at the moment we do not even have a back door! We do try to give him as much access to the garden as possible and walk him twice a day.