Return Flights Luton to Lisbon - departs Monday 2nd October / returns Wednesday 11th October - £48pp (No Bags) @ WizzAir via Google Flights

Two sets of underwear & socks. Wear one, wash/dry one.
Couple of tee shirts.
One long sleeve top.
Swim wear, wash/dry over night.
Pair of trainers and sandals.
Two lower wear. Skirts/trousers/shorts.
All of which can be worn or carried on on the plane, no bag required.
If you wear old or cheap stuff then you just leave it behind for those that need it, and come back light.

I managed 6 days with only the backpack 🎒 they allow. Went to boots in the terminal on the way to get all my washing stuff etc. surprisingly if you plan well and take all matching stuff it’s not too difficult- 9days definitely a bit harder though!!!

Just a tip. If you buy something in an airport shop they'll give you a bag, the airlines can't stop you from bringing one extra bag onboard from the airport otherwise the business model of the airport wouldn't work It's a good way to get a little bit of free hand luggage providing you can find a store or duty-free willing to give you a large-ish bag, last time I was in Alicante the duty-free bags held four 1 litre bottles so that should certainly help with the 1 bag included issue for that many days.

Shorter trips available at the same price (edited)

Checkk out tripadvior etc reviews of wizzair, they are a really awful airline. Always come up cheap as anything but I chose more expensive to avoid they are that bad

Not a good deal. Can be had for £31 last minute.

Hand baggage only (40x20x25cm)