The plug in your photos is a USA non-polarized NEMA 1-15 plug. The markings on the device indicate it is compatible with the 230 VAC @ 50 HZ mains power in the UK. You would need a simple small plug adapter and not any kind of device that also changes the voltage or the frequency.
If you do not wish to deal with even the small plug converter, you will need to purchase a complete AC power adapter with a UK plug and having a 9.0 VDC output rated for a minimum 2.0 Amps. The DC output plug on the adapter's output cord would need to be the exact same inner and outer diameter plug as on the USA adapter and have the positive output on the center pin and the negative output on the outer sleeve.
If you do not wish to deal with even the small plug converter, you will need to purchase a complete AC power adapter with a UK plug and having a 9.0 VDC output rated for a minimum 2.0 Amps. The DC output plug on the adapter's output cord would need to be the exact same inner and outer diameter plug as on the USA adapter and have the positive output on the center pin and the negative output on the outer sleeve.