What jumped out at me was the condition of the bakelite bezel; it seems unreasonably good for a 60-year-old watch. There are other folks here with much more experience with this particular variant, but I'd be very suspicious. If you compare it to this one from a dealer with pretty good reviews, I think you'll see lots of differences. Look, for example, at the Omega logo.
The caseback definitely doesn't belong with the watch. British Military W10-6645-99 watches were supplied by Smiths, Hamilton, and CWC. Not, as far as I know, by Omega.
Updated to add: Apparently Omega did supply some of these. They are definitely pricey
www.bonhams.com
Updated to add: Apparently Omega did supply some of these. They are definitely pricey

Bonhams : Omega. A stainless steel military issue automatic bracelet watch Seamaster 300, Ref165.024, Movement No.24733196, Produced in May 1967
Seamaster 300, Ref:165.024, Movement No.24733196, Produced in May 1967 24-jewel Cal.552 automatic movement, black dial with luminous baton hour markers and white inner Arabic quarters, white minute divisions, polished luminous filled sword hands and arrow tipped centre seconds, brushed and...

British Army Omega watch from the 1960s fetches over £15,000 at auction
An historic Omega watch issued to members of the British Army in the 1960s sold for a full price of £15,312 (including fees) at Fellows Auctioneers yesterday.
www.fellows.co.uk