Listed below are airlines flying to Portugal from the UK & Eire. (I’m intending to add information for other countries but haven’t had time yet).
For a link to the airline’s own website, click on the name. Also listed are where they fly to in Portugal.
UK & Eire:
British Airways – flights to/from Faro, Funchal (Madeira), Lisbon and Porto to a wide number of airports in England, Eire, Northern Ireland, Scotland and Wales.
easyJet – flights to Lisbon from Bristol, Edinburgh, Liverpool, London (Gatwick or Luton); Faro from Belfast, Bristol, Glasgow, Liverpool, London (Gatwick, Luton, Southend or Stansted); or Porto from London Gatwick; or Funchal (Madeira) to London (Gatwick or Stansted).
Ryanair – flights to Porto from London Stansted & Liverpool or flights to Faro from Birmingham, Bournemouth, Bristol, Doncaster, East Midlands, Edinburgh, Glasgow Prestwick, Leeds Bradford, Liverpool, London Stansted & Liverpool.
TAP Portugal – flights between Lisbon, Porto and Funchal (Madeira) with Aberdeen, Belfast, Dublin, Edinburgh, Glasgow, London (Gatwick or Heathrow) & Manchester. Also various internal connections.
TUI Airways – flights to Faro from Birmingham, Bristol, Cardiff, Doncaster Sheffield, East Midlands, Exeter, London (Gatwick & Stansted) and Manchester. Also flights to Funchal (Madeira) and Azores from some airports).
See also the Transport page in the Planning section for information on rules regarding airline policies regarding flying with bikes. However, please note that these may change so I would strongly advise contacting the relevant carrier for the most up-to-date rules.