HORSPWR
E*POWAH Master
Have a look at Fenix lights, I’ve got the BC30 which fits into your budget although admittedly you need to buy 18650 cells plus a charger. The rechargeable version is also available.
Fenix Flashlight, Fenix torches Bike Lights - Fenix Lights | Myfenix.co.uk
Fenix are a quality brand, I‘ve tried a good cross section of their lights when in Mountain Rescue, can’t fault them.
The neutral tint on LED lights works well for MTB’ing at night as it gives a more natural light compared to pure white LED’s, making rough stuff easier to spot.
i also use a Zebralight with a Twofish lock block for my helmet light (again neutral tint)
I can also attest that Fenix lights are some of the best I've ever used but for the life of me I don't know why they persist with those 18650 cells, much easier to have a usb charger with internal battery for their bike lights.