I have had an eye on him since we were in London.

[tufguy]

"There is a married man who has had an affair with some other lady. He along with his family used to live in London but he shifted to Virginia in the year 2014. He now lives in Virginia with his family. His son became suspicious of him when they were living in London and he has been keeping an eye on him since then."

Now he is telling this to his friend so what would he say?

"I have been keeping an eye on him since we were living in London."

"I have had an eye on him since we were in London."

Please check.

 

[emsr2d2]

"There is a married man who has had an affair. [STRIKE]with some other lady.[/STRIKE] He [STRIKE]along with[/STRIKE] and his family used to live in London but [STRIKE]he[/STRIKE] they [STRIKE]shifted[/STRIKE] moved to Virginia in [STRIKE]the year[/STRIKE] 2014, and they still live there. [STRIKE]He now lives in Virginia with his family.[/STRIKE] His son became suspicious of him when they were living in London and he has been keeping an eye on him since then."

Now he is telling this to his friend so what would he say?

"I have been keeping an/my eye on him since we [STRIKE]were living[/STRIKE] lived in London."

"I have had [STRIKE]an[/STRIKE] my eye on him since we were in London."

Please check.

See above.

There's no reason to use "with some other lady". Just say he had an affair. Everyone knows what that means (though of course he could have had an affair with a woman or a man).
I can't quite put my finger on why, but in BrE we tend to use "to keep an/my eye on someone/something" but "to have my eye on someone/something".

 

[GoesStation]

One little point jumped out at me: it's a little odd to say that someone moved from London to Virginia, just as it would be to say they moved from Philadelphia to Pakistan. In both cases, you're saying the person moved from a city to a geographically much larger place. I'd say something like the person moved from London to suburban Washington, D.C.

 

[Tdol]

who has had an affair

I think the past simple works better there as the affair is over and he has moved to a different country.