Help with identifying and dating this old Omega?

There is every chance is a Dennison cased UK market 13322 model. Not many (any?) Swiss made cases came in 9K so its bound to be local production and the marks look British. Dates from somewhere between 1946 to 1960. There will be a date letter on the inside of the caseback which will give you the exact date, the movement serial can be used too. It looks nice and original. It will have a version of the 30mm movement (later known as 26X)

We get a lot of 'Uncle' watches here but some are nicer than others.

The back comes off that model pretty easily with a case knife or pen knife, its just pressed on but I would suggest you use caution, it is easy to damage either the watch or yourself if you slip so if you are going to have a go, maybe tape up the watch a little and don't try to force it too hard. Maybe even take it to a professional if you are naturally clumsy like me, but I can manage to get press on backs off now at least.

For selling, get some photos of the insides, both movement and inner caseback then stick it on ebay with an honest description, it will find its natural level which at a guess will be around £300-450* if it is what I think it is.

*you will see similar for a few hundred more but my suggested value has factored in that it needs a service which runs to around £200, a sensible buyer will price that in too. Once serviced they fetch more like £500-650. If you are just looking to sell, don't bother servicing it yourself.

Why don't you just ask your uncle to sell it and give you the cash?

Looks like I got it spot on. Yes as you say it has the Birmingham Z hallmark is for July 1949 to June 1950. It’s a nice thing in pretty good condition and seemingly all original. There isn’t much more you need really.

So he gave you the watch a couple of weeks ago and then died. I'm very sorry to hear that. We get a lot of "uncle" watches here, and when someone immediately expresses interest in selling it, their credibility takes a hit.