We will be arriving at Terminal 4 on United Airlines at 12:05. We need to catch the 15:00 flight to Paris on British Airways. These are obviously separate tickets, and we will check in online for the BA leg before travel. We only have carry-on luggage. From Heathrow's website, we know that it will take 20 minutes to transfer between terminals. The question is whether we follow the signs to "connecting flights" upon arrival at Terminal 4 (given that we do not have to retrieve any checked-in luggage), or are we required to leave the secure area and go through immigration because we do not have a "through" ticket? If it is the latter, will 3 hours be enough to catch our BA flight?