That looks like an Octalink V1 spline, but check the BB photos here to be sure, and for a partial list of other V1 cranks.
https://sheldonbrown.com/bbsize.html
If it is in fact V1, I believe that XTR is the only Shimano MTB group that uses that spline. Still, used XTR cranks are surely out there for much less than £350. I think a road crank arm would work fine. 5502 is V1 and made in black or you could make do with silver or paint a silver 105 or Ultegra black. There were Octalink cranks made by other manufactures (Ritchey, RaceFace, Origin8, etc.) but I'd have to do some research into which spline pattern each used.
If you can't come up with an Octalink crank, I'd just put an inexpensive square taper crank (LX, FSA, etc.) in and enjoy the bike.