This is a tricky one. Essentially, BA looks at tickets separately and at check-in they usually only consider travel for what is ticketed within the BA booking/PNR. Through-check in is almost certain no, though there have been very occasional reports of BA agents (mostly outsourced outstation ones) bending the rules, but it is common knowledge that CDG BA check-in isn't always known to be the most customer-friendly, to put it politely. Similarly, saying you were only travelling Hand Baggage Only and the question of through-checked baggage wasn't going to be an issue, even then BA typically only consider and validate your travel based on your ticketed destination within your BA ticket, if you had your JL boarding pass from LHR as well as a printed copy of your onward itinerary, you might be permitted to board. However, again, I am not sure if this can be taken for granted as essentially BA would be "taking the risk" by permitting you to board as hypothetically, if one tried to enter the UK then without a valid visa and was refused, this would potentially go back to the airline in terms of a fine. Now I know you wouldn't be doing this, but it does factor into the decision making as to whether you'd be permitted or not. Now of course, say you were permitted, then all good. Having said this, there is a policy in place where Border Force can permit you entry, without a visa, if they are satisfied that you are going to leave within 24 hours and have a confirmed onward ticket, though again, this is "at the discretion" of the border officer. Again, this is dependent on BA permitting you to board at CDG. All in all, it is tricky, I believe it would be prudent to choose a more "secure/safer" option, ie. an itinerary which is all within 1 PNR, or an itinerary where visas or COVID rules wouldn't be a problem even if it weren't to be on one ticket.
There was a similar thread, in the reverse direction, ie. from LHR to CDG, whereby people had onward separate tickets from CDG, but at the time, France weren't permitting people from the UK to enter due to COVID restrictions, again it was mired with similar dilemmas as I mentioned above.
All the best
