Begin with the station you can reach cheaply
Start with your London departure point, not the airport brand. A traveller already near a Piccadilly line station can reach Heathrow without paying for a separate connection to Paddington or Victoria. Someone beside Victoria Coach Station should also check National Express, whose official London-to-Heathrow page currently advertises one-way fares from £9.50. A low headline fare stops being cheap if reaching its departure station adds another ticket and a difficult interchange.