sorry, no such thing as radial ring main. Circuit is either a radial ie 1 cable from con unit out to 1 or more points or its a ring going out around area & back to start.
A1 ring- 2.5mm2 cable max floor area per circuit 100m2. on 30/32A
A2 radial 4.0mm2 " " " " " 75m2 on 30/32A
A3 radial 2.5mm2 " " " " " 50m2 on 20A MCB
Cable length are irrelevent as if above rules followed can't be too long!
Cooker circuits & lighting circuits also radials, & lengths are governed by need to keep circuit loop impedances low enough to trip circuits fuse/MCB in less than 0.4seconds, under fault conditions.
If above followed then no limit to number of socket outlets,
In addition to previous info. for radial circuits the total length allowed depends upon type of protective device at consumer unit ie rewirable, cartridge fuse, MCB (type 1,2 B,C,D)
so if you have a specifice circuit in mind we can give definitive answer,