Please find below some help in finding a good priced flights to Faro.
There are heaps of choices, both scheduled and charter – this may save you a bit of time in trawling through all the sites!

None of these is given as a recommendation – only as a source of information

Tip 1 – if you want to go for exactly 7 or 14 days, then your cheapest option is normally a charter-unless you get in 6 months ahead.  If you want to go for, say, 3, 5 or 10 days, then you will need a scheduled flight
Tip 2 – weekday flights tend to be cheaper and you can start the let any day
Tip 3 – sign up for newsletters from the no frills airlines and they will email you when the new schedules are coming out  

This list is not exhaustive but gives you a good place to start

UK
Easyjet.co.uk from Luton, Newcastle, Stansted, East Midland, Liverpool, Gatwick, Belfast and Bristol
Jet2.com from Blackpool, Leeds Bradford,  Heathrow, Manchester

Bmibaby.com from Cardiff

Thomsonfly.com offer weekly summer flights from many UK airports and also winter from Newcastle, Bournemouth, Coventry, Doncaster Sheffield

ba.com – who fly from Gatwick

NB Ryanair only from Dublin and Brussels

Charters to try:
thomascook.co.uk
firstchoice.co.uk
XL.com
fly-monarch.com
firstchoice.co.uk
airtours.co.uk
thomsonflights.com
air2000.co.uk
mytravel.co.uk
futura-aer.com ( LGW only)
airmalta.com (BRS only)
eaac.co.uk ( Bournemouth only)

And some agents who will look at different carriers:
www.skyscanner.net
farebase.net
cheapflights.co.uk
kelkoo.co.uk
airline-network.co.uk

From Ireland, try:
www.eirjet.com
www.mytravel.com
www.ryanair.com

from the Netherlands try
www.transavia.com

from Canada try:
www.airtransat.com
www.sata.pt
www.skyserviceairlines.com

Correct at 10th Jan 2010
Note - None of these is given as a recommendation – only as a source of information