Ok so!

Not knowing the airline line I can’t comment on the terminal but it’ll either be on AC (T2) or BA (T5), on economy with no status.

This means uour main hurdle will be the immigration queue, it can be between 15 to 90 mins, however on a Sunday morning it should be on the lower side!

With no checked luggage no time wasted there!

Next steps how are you travelling between LHR and St Pancras

Choices would be
Underground (goes direct to St Pancras) however over an hour
Heathrow express to Paddington then the underground to St Pancras (can’t give a time some others on here will help though)
A car (same I can’t give times as I always take the underground or drive my own car)

say no delays and worst situation in immigration you leave the airport at 12:00, this gives you 1:52 to get to St Pancras is travelling standard or 2:12 if going business (check in closure times are 30 and 10 mins respectively)

This is easily doable, if there is no delays on the flight, immigration is not any worse, and traffic holding you up too!