Switch between two outputs on a timer
At 3.3V I assume you are using blue LEDs.

The most efficient blue LED is a Cree XPEBBL-L1 $1.20 (single qty)
This LED will operate at 10mA up to 500mA.  It is fairly bright at 10mA.





Four Cree Blue XPE LEDs @ 10mA



9V battery is a very poor choice.  A 3.6V Li-ion would be much more efficient. Do not use off brand, no name batteries as they generally do not have the advertised mAh capacity.  Panasonic is a good choice e.g Panasonic 3350mAh 18650 Li-ion 3.7v Battery NCR18650B $7 

Resistors are very inefficient and the brightness will dim as the battery discharges.

You have limited space so a small Constant Current Regulator(CCR) with an enable pin would would do very well.  It will keep the brightness constant as the battery discharges.  A Li-ion will drop from 4.2V to 3.0V as it discharges. 



On-Semi's CAT4004A an eight pin (2x2mm and 3 x 3mm packages) has four channels and a Rset pin to set the power on current. LEDs can be adjusted between 2mA to 40mA with 1.3v logic level signal.

LED Current for all 4 channels set by External Resistor and turned off and on with a single Enable pin. 

On-Semi CAT4004A Datasheet, 50 mV dropout at 20 mA, $1



A circuit with the above components would run about 90 hours @ 40mA or 335 hours @ 10mA



8 LEDs    $9.50 
Battery   $7.00
2 CAT4004 $2.00
          -----  
         $13.95 ≈ £10  


A µController to turn them off and on would be about $0.50

Using less efficient LEDs and lower capacity battery would cut the cost considerably.