Your son is British if he was born here. The only time this would differ is if he was born on a Military base…ie, my Dad was Royal Air Force and if he had been posted to Germany and taken my Mum with him and she’d given birth to me there I’d still be British. I was born up North and to some people that’s another Country altogether! 
Andrei, look on the CAB site (Citizen’s Advice Bureau) or pop along to them. They can advise you of this. As mentioned by someone else, you only have to stay in the UK for 2 weeks and prove you aren’t already married before you can legally get married here. Even if you’re English and want to get married in Scotland, some places ask you to stay there for 2 weeks or prove your family home is there. Luckily my parents home was in Scotland so I didn’t have to stay for the full 2 weeks. Gretna Green has a different policy though hence why it was the place to go to for years…I think you only need to be there for 12-24hrs before the wedding but don’t quote me on that.