17th Regulations require...

#1 Voltage drop within limits for the final circuit type.
Hence cable size must be suitable for the 35m length so as to minimise
voltage drop.

#2 All cables must have RCD protection unless Surface Run, 50mm
depth, SWA or BS8436 or Steel Conduit.
If you run FTE in the house to a jn-box then SWA up the garden, that
FTE must be surface run or 50mm depth or in steel conduit or have RCD
protection at the house-end rather than shed end. Having the RCD at
the house-end means an earth fault on the garage power would take out
the lights so you may want an emergency light in the garage if using
circular saw.
Some people run SWA all the way to the house CU, but in some cases
this can be very difficult (solid floors, space).

There is a uk.d-i-y FAQ available - worth reading.

35m is quite a long way - I assume that includes the run inside the
house to the CU.
If you dropped to 16A radial in the shed and 6A lighting you could
design for a 16A supply (16A RCBO in the house) which would probably
make 6mm SWA doable. 16A is quite reasonable unless your garage is
actually a workshop with lots of power tools in use. For 35m the
garage is most likely going to be a TT supply, ie, 2 core SWA with
garage local earth rod.