>>> it’s a swine to get to
Not necessarily. There are (in normal times, at least) direct flights from Heathrow with Azerbaijan Airlines.
For budget travel, consider these flights to Budapest as a connecting point:
From Gatwick, Southend and Manchester with easyJet ;
From Birmingham, Leeds/Bradford, East Midlands or Manchester with Jet2 ;
From Bristol, East Midlands, Edinburgh, Stansted and Manchester with Ryanair ;
From Birmingham, Edinburgh, Glasgow, Liverpool, Gatwick or Luton with Wizz Air.
Then fly with Wizz Air from Budapest to Baku.