you CAN build a burning red/bluray laser under £20 but it won't be portable. just buy an LPC-815 (red 250-300mW @ 300mA) or PHR-803T (bluray 100mW @ 100mA). power it with a benchtop PSU using DDL driver.
you can also use an old 16x or 22x DVD-RW drive, these can be purchased from ebay very cheap
there are LOTS of guides on how to do this, if you're not immature you know what you should do now. SEARCH button is your friend