AIBU to think I might actually be able to complain to Tesco's about their Abingdon customer service ?

They may well do that Monica but you would think a note left on the item ( customer left this at tills) would be a good idea.I have left both cheap and quite pricey buys unpacked at the till, and they have never ever been handed in according to the shop.
Not keen on Notcutts at all, know what you mean.

I am not defending them. I think most of the staff on information desks are disinterested and unmotivated and they are just not inclined to think that any spare goods found lying around might have been left behind by mistake. If everything left on the counter had to be written in a book or logged into a computer, staff could just check. I have been in stores where if I think I have left anything behind they immediately refer to a lost/left behind record book and can give me a definitive answer.

Yes, most stores and shops do keep any left by mistake goods, at least for a while.
Remember the lost luggage counters in rail stations, I remember once going there as I had left a blue umbrella on the train, and the attendant brought about ten for me to choose from.

A couple of years ago,I went into my local Tesco Extra branch. As I walked past the customer service counter,I heard the member of staff say to the customer standing there 'The customer service desk is out of order'. With that she placed an 'out of order' sign on the counter.

?

Sounds more like the staff member was out of order..

I find that if I go on Twitter to complain about something it always gets a response.