Charging facilities at Terminal at Luton Airport are somewhat limited, with a current traveller rating of 5/10. The most reliable spots for charging are located around Gate 17, where you can find a couple of waiting rooms equipped with plug-in points suitable for UK plugs, although they are not situated right next to seating. Additional charging points are available by the gates, but they are positioned on the floor rather than near the chairs, which may be inconvenient for some. Be sure to plan ahead and keep your devices charged, as the options for charging are scarce.
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There aren't many charging points. Around Gate 17 looks like the best bet. There are a couple of waiting rooms there that have plug-in charging points (for UK plugs, not USB sockets). They're not right next to chairs though.