Essentially you have 3 holes into the underfloor void:
- 2x light switch oval conduit, 1x light ceiling rose

Underfloor void is typically:
- Runs of joists, separated by oblong or X-strap blocking
- Oblong blocking may "occlude" cable rod access if joist offcuts
- Joists may be of differing depth per room depending on span

You need cable access rods &/or cable tape, plus chain & magnet.
You need access to the underfloor void "somewhere" - typically the
stair landing or box-room or some other small bedroom.

Typically push a short cable rod with loose chain up the conduit or
ceiling rose hole so the chain dangles on the plasterboard. Then push
lengths of cable rod/tape with magnet on the end along the "duct"
formed by the joists/floor/ceiling until you hear the chain snap to
the magnet. You may have to twirl the access rods holding the chain.
When you hear it snap, unscrew the chain from the access rod & tie on
a piece of string, withdraw the other access rods to pull through the
string then cable.

Alternatively you could try a flexible cable tape pushed up which
eventually makes its way along the ceiling void, this is usually quite
difficult - but go with what works with any given situation.

You will probably need to drill holes to "cross" joists from the other
light switch.

The only other alternative is to use MK Echo (or similar) wireless
light switches & receiver at the ceiling rose, or an occupancy sensor
and dispense with conventional light switches (might be buying a spare
occupancy sensor if ever going cheap).

There are true "extending fishing rod" access rods which are used in
lofts from the loft hatch to feed cable around ceiling rose & oval
conduits. They are quite expensive, about £76, but work incredibly
well - you just poke rods with long flexible chain up the ceiling rose/
switch drop and use the rod to snap onto them, typically with end-
mounted LED & magnet (double fitment).

Most cable access rod kits lack the flexible open-link chain, but you
can make one and open a link to feed it through an "eyelet" fitting on
the cable access rod. You need steel chain, not brass, for magnets to
work. Glue the magnet if it feels loose, the Silverline ones tend to
be quite strong but poorly retained in the fitting (nothing more than
a weak interference fit).

Cable access rods do not conform to the same thread standard, do a
Google on a previous post. You can also buy "magnet on bendy-rod to
handle" - quite useful but the magnet head is too large. Beyond that
the next tool is a boroscope camera, such as a USB type or the type
with LCD display on the other end (no PC/laptop required).
Electricians in a hurry will rip down a ceiling as it is quicker if
you have walls on floors or tanks on floors preventing access, only
needs some pieces of plasterboard and a skim.