That's my neighborhood in London.
The Pembroke is on Old Brompton Rd. They serve until 9 PM and if it's a nice day have a rooftop garden you can dine in. It's an independent pub.
The Kings Head, 17 Hogarth Rd., is just a one minute walk off Earls Court Rd. As stated, it's a Fuller Pub, one of three on or just off Earl's Court Road, but this one seems better than the others. It serves until 9:30 PM.
The Blackbird has just been completely renovated. I haven't been in since the completion. (They also just started renting out rooms.) They are known for their pies. They are located on the corner of Earls Court Rd and Barkston Gardens.
Both the Kings Head and the Blackbird are about three minutes from the Earls Court Tube Station.
The Courtfield is directly across the street from the Earls Court Tube Station on the corner of Earls Court Rd and Earls Court Gardens. I have never been in there, even though I've passed it hundreds of times, so I can't give you an opinion.
But if you want a pub that caters more to locals than to tourists, try the Devonshire Arms at 37 Marloes Rd. It's just a few minutes walk north of Cromwell Rd. I have never had Sunday lunch there but they serve food well into the evening.
If you tell me where you are staying I can give you walking directions to any of them.
Whatever you do, stay away from the Prince of Teck. Not only are they rude their food isn't that great.