Old gold Omega watch - is it real?

Looks good to me

The bracelet reminds me of one I bought from the UK - do you happen to live in the UK?

You will have to let the watch be opened by a professional and take good photos of the movement and the inner side of the caseback.
And don´t forget to write down the serials - a back up in case the photos are not that great...

Then the experts will be able to tell you more.

The case look very like that used on the UK market Dennison 13308 Omega, right down to the lug hallmark. It probably houses a 501 movement and dates to the mid 1950s. As already noted it has certainly been redialled. The bracelet as noted above is UK market also, manufactured by the Shackman company of London. Here is what a a similar model, different only slightly in dial detail looks like:

Whatever you do, please do not be tempted to sell the bracelet for scrap gold weight. Bracelets like these (although not very popular for daily wearers as they are out of fashion), are not easy to find anymore and are a great part of horological history- they were a statement piece. Even if you sell the bracelet for only the gold value- please see that it goes to an Omega watch collector.
That is of course unless you choose to wear it as is, then flash that bling with a gold pinky ring and a Gaberdine suit.

Indeed! I do apologise, I read the bracelet hallmark as DS&S, in fact you are right it's JG&S. This is in fact John Grinsell & Son, meaning both case and bracelet were made in Birmingham (as was I) The case is almost certainly Dennison though IMO.