Ive done a lot of this work on proerties ive developed, usually on ceilings of over 9 foot in height with deteriorating lathe and plaster...
Use 3x2" cls/scant to run a rail level around the room fix with hammer/frame fixings.
The cross battoning to be done with the same timber with centres fixed for fixing plasterboard. If your working by yourself its best to use handiboard which is 900mm by 1220mm. you should have a x latticework with centres to butt plasterboard together. use a string line to make sure that all of the centres are equally spaced.
the lattice work should be fixed thru to the existing joists to stop it from sagging or flexing. use short pieces of off cut 3x2 fixed with 4"(10s/12s) screws to fix flat thru the plaster into the joists. cut legs of timber to fix lattice to these off cuts (fixed to existing joists)
make sure that all screws underneath are countersunk so that the pasterboard aint damaged when you fix it.
before you fix the plasterboard turn off the lecky and unscrew the ceiling rose on the light fitting(s). Dont tug hard on the lighting cable... sometimes it has a nasty habit of damaging connections to junction boxes and ya doont wanna start taking up boards in the floor above! If enough spare cable pulls through your ok. if not, it will need extending.
You will have to use 1.5mm twin and earth cable. Note that if there is no earth wire (and on sum 50s 60s 70s builds there often isnt
you should only use plastic light fittings unless you installl supplementary earth bonding.... if in doubt consult a qualified electrician. You might want to install additional ceiling lights. Ask an electrician's advice as this will require figuring out how the existing ceiling rose has been wired.
offer up the pasterboard and fix with min 25mm dry wall screws. Try and get the butt joints as close together or you'll end up having to fill the gaps with plaster before applying the finishing coat. Accurately drill hole for light cable and introduce cable thru hole and fix board Cover all screw heads and tape along all joints with self adhesive scrim tape.
Apply finish coat of plaster.
good luck.Would be interested to find out how you got on