score:6
You will NOT be allowed travel on this itinerary. You will be denied boarding at your point of origin.
Current regulations disallow most travelers from entering the US if they have been "physically present" in any of a number of countries within 14 days prior of their entry to the US - and this list includes the UK.
For the purposes of these regulations, being in transit is considered being "physically present" in the country.
As you are attempting the enter using a H-1B visa, you are almost certainly not covered by any of the exceptions for this rule. The airline will realize this at your original point of departure, and not allow you to board the flight to the UK.
Upvote:2
According to https://www.britishairways.com/en-us/information/incident/coronavirus/entry-requirements the following applies to airside transits for destinations outside the Common Travel Area:
For destinations in the rest of the world (outside the Common Travel Area), you wonβt need to stop your journey. Youβre still able to connect flights at London Heathrow, Gatwick or any other UK airport, but you must stay airside (do not pass border control) and go straight through Flight Connections. If you do not pass border control, you will not need to quarantine. You still need to comply with the entry requirements for your final destination.
So yes, your itinerary is currently allowed, as far as UK Covid travel rules are concerned. The USA is a different matter.