I'm assuming that you mean LHR (London Heathrow) instead of HEA.

When you're upgrading from one cabin to a higher cabin using Avios then you will pay the additional taxes, fees and carrier charges for the higher cabin. That's always been the case. The carrier charge component of that can be very high - especially on itineraries departing the USA. I really now struggle to justify using Avios for upgrades.

Instead I have redeemed a lot with Iberia where (a) the Avios required for a flight tends to be less than on BA and (b) the cash component is a lot lower too. I also redeem Avios for short-haul flights within the UK and Europe, and also for domestic flights within the USA with both AA and Alaska. The co-pay for those flights is just a few dollars.

One good use of Avios is for last-minute redemptions where the cash fare is high. Avios bookings also give you the flexibility to cancel for a $55 penalty up to 24 hours before your flight departs.