For a midday international departure, our model's typical (median) door-to-gate time at Heathrow is about 118 minutes, rising to around 145 minutes on a busier-than-usual day - not counting your journey to the airport itself.
Heathrow is about 24 km west of central London. The Heathrow Express takes about 15 minutes from Paddington; driving or a taxi typically takes 45-90 minutes depending on traffic - a wide range, and worth checking on the day rather than assuming the fast case.
Terminal 5 is exclusively British Airways; Terminal 2 hosts Star Alliance carriers; Terminal 3 hosts Oneworld and other international airlines. Confirm yours before you plan your route to the airport.
These are general, statistically-modelled estimates - not a guarantee. Always allow extra time for anything unusual, and check your airline's and airport's own current guidance.